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					         An AIlirmatite Action/EqualOpportunityEmplo}er




I




    CompositionbySharonL. Hurdle,GroupQ-4,
        and PamelaH. Mayne,Group IS-6
                                                                      NUREG/CR-3678
                                                                      LA-1OO38

                                                                      RS




               EstimationMethods for Process Holdup
                    of Special Nuclear Materials



                                 K. K. S. Pillay
                                  R. R. Picard
                                 R. S. Marshall




                         Manuscriptsubmitted: Februaty 1984
                            Date published: June 1984
     —   ---
                                       L r’    ..   .“   . .

                                       Prepared for
                               Safeguards Research Branch
                               Divisionof FacilityOperations
                          Office of Nuclear RegulatoryResearch
                           US Nuclear RegulatoryCommission
                                  Washington, DC 20555
                                 -.... .., -
                                  NRC FIN No. A7~26               -

I



I

    LosAlamos                                        LosAlamos National Laboratory
                                                     LosAlamos,New Mexico 87545
                                          ExecutiveSummary

   This is the final report on a research program sponsoredby the SafeguardsResearch Branch of the
Nuclear Regulatory Commission(NRC) to explorethe possibilitiesof developingstatisticalestimation
models for residualholdup of highlyenriched uranium (HEU) at processingfacilities.This study was
initiated as part of an effort to refocus the resources of materials control and accountingfor timely
detectionof specialnuclear material (SNM) loss. Throughout this investigation,periodicreports of the
status of the study weresubmittedto the NRC, and thisreport is a compilationof allthework doneduring
the project.A formalreport on this project,titled“UraniumHoldup Modeling,”was issuedin 1983.It is a
                                                     the
genericreport on holdupestimationthat highlights valueof predictivemodelsfor estimatingquantities
of materialsand their variances.
   The task of gathering holdup information and the developmentof holdup estimators for specific
processes underwent several stages of examination. Historical data available from HEU-processing
                                                                          w
facilities,whichweregatheredas part of periodicinventorydevelopment, ereconsideredfwstas a readily
availablesourceof long-termholdupdata. The poor qualityof thesedata made this sourceof information
                                                   T
of limitedvalueto statisticalmodeldevelopment. he next step in gatheringgood-qualityholdupdata was ,
through carefullydesignedmeasurementsof SNM holdupat two of the materials-processing           facilitiesof
the Los Alamos National Laboratory. Selectedmeasurementsconductedover a period of 1 yr showed
that certain equipment, such as air filters and calciners, lend themselves to good-quality holdup
                                                          d
measurementsand have potentialsfor estimation-model evelopment.Attemptsto developthese holdup
data without interferencewith plant schedulesimposedlimitationson the quality of some of the data
                                                H
gatheredduringthisphaseof the investigation. owever,thesemeasurementsdidprovidevaluabledata on
holdup of uranium and plutoniumon exhaust air filtersunder severaloperatingconditions.The holdup
estimationmodelsdevelopedfrom thesedata formed a sound basis for developingestimationmodelsand
demonstratedthe need for good-qualitydata gathered under reasonably stable conditions.The value of
thesemodelswas furtherconfiimedwhencontrolledexperimentswereperformedusingradioactivetracers
and high-qualitydata collection.
   The next step in the directionof improvingthe qualityof holdupdata was the designand performanceof
a seriesof controlledexperimentsto simulateseveralunit processescommon to HEU processfacilities.
Two of theseexperimentswereconductedoutsideof Los Alamosunderthe supervisionand controlof Los
Alamos personnel.One of the controlledexperimentson uraniumdust generationwas performedat the
San Diego facilities of GA Technologies,Inc., and the other experiment on uranium inventory
development,in liquid-liquidextraction pulse columns, was conducted at the Allied-GeneralNuclear
Servicesplant at Barnwell,South Carolina. All the other controlledexperimentswere conductedat Los
Alamosand weredesignedto measureuraniumholdupas a functionof throughputduringfeeddissolution
processes, ammonium diuranate precipitationand calcination,and the circulationof uranyl solutions
through pipes and pipefittings.The total throughputof uranium in these experimentalfacilitiesranged
from 50 kg to -50 tonnes.
   The qualityof measuredholdupdata duringthesecontrolledexperiments(exceptfor the pulse-column
experiments)was improved by at least an order of magnitudeby using carefully selectedradioactive
tracers. These tracers, at concentration levels of -lppb, were homogeneouslyincorporated into the
processmaterials.The tracers withtheirhighspecificactivityand uniquegamma-emission          characteristics
providedthe additionaladvantage for improvingthe quality of the holdup data. Considerableattention
was paid duringtheseexperimentsto fabricateinstrumentcalibrationstandardsthat werecompatiblewith
the equipmentmeasured and the distributionof holdup within the equipment.This also contributedto
                                                          n
improvingthe qualityof holdupdata from nonintrusive, ondestructiveassays(NDAs) usinggamma-ray
spectrometry.
   Developmentof statistical models for HEU holdup used a variety of techniquesincludingmultiple
regression, Kalman filtering, and response surface methodology. Uranium holdup in glove boxes,
ductwork, air filters, calciners, precipitators, falterfunnels, rotary drum filters, feed dissolvers,pulse

                                                                                                              v
     columns,and pipes and pipetittingsof uranium circulationsystemswere measured.The models,in most
     cases, demonstrated the value of statistical models developed from good-qualitymeasurementsfor
     estimatingboth present and future residualholdup as a functionof materialthroughput.The findingsof
     this investigationrevealed that several factors such as the layout of pipes, corrosion of construction
     materials,concentrationsof solutions,and so forth impactholdupof materialsin processingfacilities,and
     in many instancesthe holdupof SNM is not simplya functionof the materialthroughput.In addition,this
     investigationhas been able to identifyboth the advantagesand limitationsof holdupdata and estimation
     modelsdevelopedfrom a varietyof data-gatheringapproaches.One of the uniqueadvantagesof theuseof
     statisticalmodelsis that data necessary for updating the modelscan be gathered duringplanned plant
     shutdownconditionswithoutmajor disruptionof productionschedules.
        SectionI is an introductionto this study and its evolutionincludinga briefsurveyof presentknowledge
     on materialsholdup.SectionII highlights   someof the successfulattemptsto measureand useholdupdata
     from operatingprocessfacilitiesand the advantagesand limitationsof thesemeasurementsfor developing
     predictivemodels.
        SectionsIII-VI describethe controlledexperimentsand the details of model developmentspecificto
     each type of equipmentused during these experiments.Various designsof experiments,adaptationsof
     instruments,calibration standards fabrications,and the use of mathematicaltechniquesfor developing
     functionalrelationshipsbetween holdup and throughput are discussed.Cleanout measurementswere
     incorporated routinely into these controlled experimentsto evaluate NDA measurements. Various
     approachesto improvethe qualityof holdupdata are mentionedthroughoutthese sections.
        Section VII summarizes the findings of this investigationand highlightsthe value of controlled
     experimentsand modelingfor the developmentof holdup estimators.The potentialapplicationsof the
     holdupestimationtechniquesto fuelcyclefacilitiesand the conclusionsderivedfrom variousobservations
     are also included.
        The major findingsof this investigationare the following:
        1. Measurementof the residualholdupof SNM at largeprocessingfacilitiesis a difficultproblemand
           willremain so becauseof the inherentlimitationsof plantlayout and NDA techniques.
        2. It is often difllcultto assign a high priority for holdup estimation,which also contributesto the
           inherentproblemsof holdupmeasurement.
        3. Statisticalestimationmodelscan assistplantoperatorsin meetingregulatoryrequirementsof holdup
           estimationas part of periodicinventorydevelopment.
        4. The developmentof usefulpredictionmodelsof holduphingeson the qualityofdata and the stability
           of process operations.
        5. There are severalapproachesto improvingthe qualityof measurementsusingbetterinstrumentation
           and better calibration standards and through the application of carefully chosen secondary
           measurement techniques. If there are no improvementsin the quality of measurements,it is
           unrealisticto expectstatisticalmodelsto provideestimatesof highquality.
        6. Holdup estimation models require periodic updating to remain useful as facilitiesand process
           variableschange.
                                      to                                            f
        7. Significantimprovements holdupmeasurementsand data development or holdupestimationscan
           be accomplishedif this problemis addressedduringthe designstagesof a plant to incorporatethe
           featuresnecessaryto accomplishthe measurementgoals.
        AppendixA treats in detailthe potentialsand limitationsof the use of tracers to improvethe qualityof
                                                              by
     holdupmeasurements.This discussionis supplemented someof the resultsof preliminaryinvestigations
     to determinewhether the tracers chosen truly representthe SNM during all phases of the unit process.
     Appendix B provides introductory information on two of the mathematical techniques—regression
     analysis and Kalman filtering-used repeatedly during this study for the developmentof statistical
     estimation models. Appendix C is a compilationof the results of controlledexperiments.These are
     presented in a concise fashion to conservespace and to provideenough detailsfor those who wish to
                                                              o
     examinethe approachesdescribedfor the development f good-qualitydata for holdupmodeling.

vi
                                                CONTENTS

A13STRACT. . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

  I. INTRODUCTION . . . . . . . . . .            .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .     1
     A. Survey ofPresent Knowledge . . .         ,   .   .   .   .   .   ,   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    2
     B. Backgroundto This Investigation ,        ,   .   ,   .   .   .   .   ,   .   .   .   ,   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    3
     C. This Report . , . . . . , . . . . . .    .   .   .   ,   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .3

 II. HOLDUP MEASUREMENTSAT PROCESSING FACILITIES                                                                 .   .   .   . .     .   .   .   .   .   ,   .   .   .   ,    3
     A. MeasurementTechniques . . . . . . . . . . . . . . . . . . . . .                                          .   .   .   . .     .   .   .   .   .   .   .   .   .   ,    4
     B. Holdup MeasurementResults . . . . . . . . . . . , . . . . . . .                                          .   .   .   . .     ,   .   .   .   .   .   .   .   .   .    5
        1. PlutoniumFacility Filter Holdup . . . . . . . , . . . . . . ,                                         .   ,   .   ..      .   .   .   .   .   .   .   ,   .   .    5
        2. Uranium Scrap RecoveryFacilityAir Filter Holdup . . . .                                               .   ,   .   . .     .   .   .   .   .   .   .   .   .   .    5
        3. Uranium Holdup in Batch Calciners . , . . . , . . . . . . .                                           .   .   .   , .     .   ,   .   ,   .   ,   .   .   .   .    5
        4. Precipitatorand Rotating Drum FilterHoldup . . . . , . .                                              .   .   .   , .     .   .   .   ,   .   .   .   ,   .   .    5
        5. Uranium Holdup in Air Ducts . . . . . . . . . . , . . . . .                                           .   .   .   . .     .   .   .   ,   .   .   .   .   .   .    5
     C. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . , . .                                     ,   .   .   . .     .   .   .   .   .   .   .   .   .   .    8

III. EXPERIMENTAL STUDY OF URANIUM HOLDUP IN A DUST-GENERATING                                                                                                           FA-
      CILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                               . 13
     A. Facility Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                 , 14
     B. ExperimentalProcedures . . . . . , . . . , . . , . . . . . . . . . . . . . . . . . . . . . .                                                                     . 16
         1. Tracer Application . . . . . . . , . . . . . . , . . . . . . . . . . . . . . . . . . . . . .                                                                 . 16
        2. Measurements . . . . . . . . . . . . . . . . , . . . , . . , . . . . . . . . . . . . . . .                                                                    . 17
     C. Dust Generation and Holdup Measurements . . . . . . . . . . . , . . . . . . . . . . . . .                                                                        . 17
     D. ExperimentalResults and Discussion . . . . . . . . . . . , , . . . . . . . . . . . . . . . .                                                                     . lg
     E. Modeling . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . , . . . . . .                                                                 . 22
         1. The Filter . . . . . . . , . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . .                                                               . 22
        2. Elbows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                  . 23
        3. The Glove Box Floor . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . .                                                                     . 24
        4. The Verticaland HorizontalDucts . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                       . 27
        5. Modelingthe Glove Box System . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                                        . 33
        6. Comparison of Experiments . . . . . . . , . . . . . , . . . . . . . . . . . . . . . , . .                                                                     . 34

[V. EXPERIMENTAL STUDY OF URANIUM HOLDUP                                                     IN A            LIQUID-LIQUID                               EXTRAC-
    TION PULSE COLUMN . . . . . . . , . . . . . . . . . .                                    . . . .         . . . . . . . . . . .                       . . . . . 35
    A. Experimental Study . , . . . . . . . . . . . . . . . . .                              . . . .         . . , . , . . . . . .                       . . . . . 36
    B. Equipmentand Facilities . . . . . . . . . . . . . . . . .                             . . . .         . . . . . . . . . . .                       . . . . . 36
    C. ExperimentalProcedures . . . . . . . . . . . . . . . .                                . . . .         . . . . . . . . . . .                       . . . . . 36
                                      of
   D. Uranium ConcentrationProfides PulseColumns . .                                         . . . .         . , . . . . . . . . .                       . . . , . 38
    E. Pulse-ColumnInventoryEstimation . , . . . . . . . .                                   . . . .         . . . . . . . . . . .                       . . . . . 38
       1, Model Development . . . . . . . , . . . . . . . . .                                . . . .         . . . . . . . . ,. ,                        . . . . . 41
       2. Profde Approximationby RegressionMethods . .                                       . . . .         . . . . . . . . . . .                       . . . . . 42
       3. EstimationBased on TheoreticalConsiderations .                                     . . . .         . . . . . . . . . . .                       . . . . . 45


                                                                                                                                                                                   vii
        V. EXPERIMENTAL STUDY OF URANIUM HOLDUP                                                                       DURING                                 AMMONIUM
           DIURANATE (ADU) PRECIPITATION AND CALCINATION                                                               . . . . . .                       .   . . . , . , .51
           A. Experimental Study . . . . . . . . . . . . . . . . . . . . . , . .                                     . . . . . . .                       .   , . . . . . . 51
           B. Facility Description . . . . . . . . . . . . . . . . . . . . . . . .                                   . . . . . . .                       .   . . . . . . . 53
           C. Holdup Measurements . . . . . . . . . . . . . . . . . . . . . . .                                      . . . . . . .                       ,   . . . . . . . 53
          D. ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . .                                     . . . . . . .                       .   . . . . . . . 56
           E. MaterialsBalanceand CleanoutMeasurements . . . . . . . . .                                             . . . . . . .                       .   . . . . . . . 58
           F. Residual Holdup Estimation . . . . . . . . . . . . . . . . . . . .                                     . . . . . . .                       .   . . . . . . . 60
              1. Calciner Trays . . . . . . . . . . . . . . . . . , . . . . . . .                                    . . . . . . .                       .   . . . . . . . 6(I
              2. Feed Dissolver . . . . . . . . . . . . . . . . . . . . . . . . .                                    . . . . . . .                       .   . . . . . . . 6I
              3. Filter Funnels . . . . . . . . . . . . . . . . . . . . . . . . . .                                  . . . . . . .                       .   . . . . . . . 62
              4. Calciner . . . . , . . . . . , . . , . . . . . . . . . . . . . . .                                  . . . . . . .                       .   . . . . . . . 63
              5. precipitator . . . . . . . . . . . . . . . . . . . . . . . . . . .                                  . . . . . . .                       .   . . . . . . . 65

       VI. EXPERIMENTAL STUDY OF URANIUM INSOLATION                                                      LOOPS                           .   .   .   .   .   .......67
           A. Facility Description . . . . . . . . . . . . . . . . . . . . .                             . . . . .               .       .   .   .   .   .   . . .0 .             .   .67
           B. ExperimentalProcedures . . . . . . . . . . . . . . . . . .                                 . . . . .               .       .   .   .   .   .   . . . . .            .   .69
           C. Holdup Measurements . . . . . . . , . . . . . . . . . . . ,                                . . . . .               .       .   .   .   .   .   . . . . .            .   . TO
          D. Experimental Results . . . . . . . . . . . . . . . . . . . . .                              . . . . .               .       .   .   .   .   .   . . . . .            .   . 70
           E. Modeling . . . . , . , . . . . . . . . . . . . . . . . . . . .                             . . . . .               .       ,   .   .   .   .   . . . . .            .   .72

       VII. DISCUSSION AND CONCLUSIONS                   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .       .       .   .   .   .   .   .    .   .   .   .   ..80
            A. Value of ControlledMeasurements .         .   .   .   .   ,   .   .   .   .   .   .   .   .   .   .   .   .       .       .   .   .   .   .   .    .   .   .   .   . . 81
            B. Motivationfor Modeling . . . . . . .      .   .   .   .   .   .   .   ,   .   .   .   .   .   ,   .   .   .       .       .   .   .   .   .   .    .   .   .   .   , . 82
            C. Applicationsto Fuel Cycle Facilities      .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .       .       .   .   .   .   .   .    .   .   .   .   . . 83
           D. Conclusions . . . . . . . . . . . .“. .    ,   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .       .       ,   .   .   .   .   ,    .   .   .   .   . . 84
       ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

       REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

       APPENDIX A: USE OF TRACERS IN MATERIALSHOLDUP STUDY.                                                                  .       .   .   .   .   .   .    .   .   .   .   .   .    89
         I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                            .       .   .   .   .   .   .    .   .   .   .   .   .    89
        II. EXPERIMENTALSTUDIES USING TRACERS . . . . . . . . . . .                                                          .       .   .   .   .   .   .    .   .   .   .   .   .    89
            A. QualitiesOfaTracer . . . . . . . . . . . . . . . . . . . . . . . . . .                                        .       .   .   .   .   .   .    .   .   .   .   .   .    90
            B. Tracers Usedin HEU Holdup Measurements. . . . . . . . . . . .                                                 .       .   .   .   .   .   .    .   .   .   .   .   .    91
            C. Limitationsof ExperimentalFacilities . . . . . . . . . . . . . . . .                                          .       .   .   .   .   .   .    .   .   .   .   .   .    92
            D. Tracer Levelsand MeasurementMethods. . . . . . . . . . . . . .                                                .       .   .   .   .   .   .    .   .   .   .   .   .    92

        111. RESULTSAND DISCUSSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
            A. Homogenizationof Tracers in Uranium Matrices. . . . . . . . . . . . . . . . . . . . . . . 94
            B. NDAs and Cleanout Measurementsfor Holdup Determination. . . . . . . . . . . . . . . 94

       REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

       APPENDIX B:PRINCIPLESOF REGRESSIONAND KALMANFILTERING . . . . . . . . . . 97

          1. REGRESSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
         II. KALMANFILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

       REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

       APPENDIX C: DETAILED DATA FROM CONTROLLED EXPERIMENTALSTUDIES . . .                                                                                                            100
 ...
Vlu
                                              TABLES

      I.  Holdupof Plutoniumon a GloveBoxAir Filter . . , . . . . . . . . . . . . , . . , , . . .6
     II.  Holdup of Uranium on ExhaustAir Filtersat TA-21 . . . . . . . . . . . . . . . . . . . .7
    HI.   Grams of UraniumHoldup for CalcinersWeightedby MaterialProfiles . . , . . . . . . .7
    Ive   Locationsof MeasurementPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
     v.   ExperimentalConditions . , . . . . . , . . . . . . . . , . . . . . . . . . . , . . . . . . . 18
    VI.   Comparisonof Model-BasedEstimateswith Weight-LossValues . . . . . . . . . , . . 21
   VII.   A Comparisonof HoldupEstimatesby DifferentMethods , . . , . . . . . . . . , . . .21
  VIII.   Summaryof ModelingResultsfor Low-AirflowExperimentwith Uq08 . . . . . . . ..34
    IX.   Pulse-ColumnOperatingConditions . . . . . . . . . . . . . . . . . . . . . . . . . . . , 38
     x,   Summary of ModelingResults . . . . . , . . . . . . , . . . . . . . . . . . . . . . . . . .46
    XI.   EstimatedConcentrationProfiles . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . 50
   XII.   ExperimentalParametersof ADU Precipitationand CalcinationExperiments . . . . . 56
  XIII.   Comparisonof NDA Measurementsof Holdup with CleanoutMeasurements . . . . . 59
   XIV.   Holdup Estimatesand CleanoutValuesfor the ADU Experiment . . . . . . . . . . . . 66
   xv.    ComponentDescriptionand ExperimentalParameters of CirculationLoop . . , . . . .69
  XVI.    CleanoutMeasurements—Uranium        SolutionLoop Experiments . . . . . . . . . . . . . 71
  XVII.   Values of MeasurementVariability(c# and Process Variability(c$) Used in Filteringthe
          SolutionLoop Data . . . , . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . .72
     A-I. SpecificActivitiesof 235U Tracer Isotopes . . . . . . . . . . . , . . . , . . . . . . .91
                                   and
    A-11. Tracers and Their CompatibleForms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
   A-III. Per Cent Tracer Found at VariousStagesof ADU Precipitationand Calcination . . . . 95
   A-IV. Comparisonof NDA Measurementsof Holdup with CleanoutMeasurements . . . . .95
     C-I. Summaryof ModelingResultsfor Medium-Airflow          Experimentwith U308 . . . . . . 101
    C-IL Summaryof ModelingResultsfor High-AirflowExperimentwith U30g . . . . . . . . 101
   C-III. Constants of Integration . . . . , . . . . . . . . . . . . . . , . . . . . . . . . . . . . . 102
   C-IV. Table of MeasuredHoldup Per Unit Area . . . . . . . . . . . . . . . . . . . . . . . . 102
    c-v. Table of MeasuredHoldup Per Unit Area . . . . . . . . . . . . . . . . . . . . . . . . 102
   c-w. Table of Measured Values . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
  C-VII. Table of MeasuredHoldup Per Unit Lengthof Ductwork . . . . . . . . . . . . . . . . 103
 C-VIII. Table of Holdup Measurements . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
   C-IX. Summaryof ModelingResultsfor Experimentwith Coarse Uq08 . . . . . . . . . . . 104
    c-x. Table of Holdup Measurements . . . . . . . . , . . . . . . . . . . . . . . . . . , . . . 105
   C-XI. Summaryof ModelingResultsfor Low-AirflowExperimentwith Ash . . . . . . . . . 105
 C-XII. Table of Holdup Measurements . . . . . . . . . . . . . . , , . . . . . . . . . . , . . . 106
C-XIII. Summary of ModelingResultsfor Medium-Airflow            Experimentwith Ash . , . . . . . 106
C-XIV. Table of Holdup Measurements . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . 107
  c-xv. Summaryof ModelingResultsfor High-AirflowExperimentwith Ash . . . . . . . . . 107
 C-XVI. ConcentrationProfileData . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . 109
C-XVII. ConcentrationProfileData . . . . . . . . . . . . . . . , . . . . , . . . . . . . . . . . 109


                                                                                                             ix
                                                      TABLES (cent)


         C-XVIII.   Holdup of Uranium in the PrecipitationColumn . , . . , . . . . . . . . . . . . . . . . 1I 1
          c-x1x.    Holdup of Uranium in the Filter Funnels . . . . . . . . . . . . . . . . . . . . . . . . . I I 1
           C-xx.    Holdup of Uranium in Calciner . . . . . . . . . , . . . . . . . . . . . . . . . . . . . , 112
          C-XXI.    Holdup of Uranium in CalcinerTrays . , . , . . , . . . . . . . . . . , . , . , , . . .         112
         C-XXII.    Holdup of Uranium in the DissolverVessel . . . . . . . . . . . . . . . . , . . . . . . .       113
        C-XXIII.    Data from SolutionLoop Experiments:CPVC Loop, Low Flow Rate . . . . . . . . .                  115
        C-XXIV.     Data from SolutionLoop Experiments:CPVC Loop, High Flow Rate . . . . . . . .                   115
         c-xxv.     Data from SolutionLoop Experiments:StainlessSteelLoop, IAw F1OW              Rate . . , . .    116
        C-XXVI.     Data from SolutionLoop Experiments:StainleesSteelLoop, High F1OW             Rate . . . .      116
        C-XXVII.    Holdup Estimatesfor Each MeasurementLocation at the Conclusionof the
                    Experiment . . . . . . . . . . . . , . . . . . . . . . . . , . . . . . . . . . . . . . . . .   117




I




    x
                                               FIGURES

Fig. 1.                                                                               I
         Total holdupof uraniumin four duct systemsat GA Technologies, nc. . . . . . . . . . .8
Fig. 2,  Measurementhistoryof the holdupof plutoniumon an air filterat TA-55. . . . . . . . .9
Fig. 3.  Measurementhistoryof the holdupof uraniumon air filterDB-1. . . . . . . . . . . . . 10
Fig. 4.  Measurementhistory of the holdupof uraniumon air falterDB-30. . . . . . . . . . . . 10
 Fig. 5. Measurementhistoryof the holdupof uraniumon air filterDB-24. . . . . . . . . . . . 11
 Fig. 6. An isometricviewof the experimentalfacility. . . . . . . . . . . . . . . . . . . . . . 0 . 15
 Fig. 7. A schematicof the dust-generationapparatus. . . . . . . . . . . . . . . . . . . . . . . . 16
 Fig. 8. Change in holdup as a functionof throughputof fine U3013 powder at the exhaust ~r filter                  .
          (measurementlocation 14). . . . . . . . . . . . . . . . . . . . . . ...........020
 Fig. 9. Change in holdup as a functionof throughputof tine U3Q powder at the firstelbowof the
          ductwork (measurementlocation 8). . . . . . . . . . . . . . . . . . . . . . . . . . . . ..20
Fig. 10. Holdupof uraniumon the filterfrom the dust-generationexperimentat low airflow. . . 23
Fig. 11. Holdup measurementhistory (for the low-air-flow            experimentwith U~OJ at measurement
          location 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
Fig.12, Three detectorssuspendedover a glovebox floor. . . . . . . . . . . . . . . . . . . . . .25
Fig. 13. A singledetector over (Xl,yl). . . . . . . . . . . . . . . . . . . 0 0 0 0 . . . 0 . 0 “ “ o 026
Fig. 14. Measurementson the glovebox floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
                                                           s
Fig. 15. Sphericalcoordinatesin three-dimensional pace. . . . . . . . . . . . . . . . . . . . . . 28
Fig. 16. Sideviewof detector and verticalcylinder. . . . . . . . . . . . . . . . . . . . . . . . . . 29
Fig. 17. Overheadviewof detector and verticalcylinder. . . . . . . . . . . . . . . . . . . . . . . 30
Fig. 18. Measurementson the verticalcylinder. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
 Fig. 19 Holdup measurementhistory(for low-airflowmeasurementswith Ug08) at locations 11-13.
            . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Fig. 20. A schematicrepresentationof the pulsecolumnsused. . . . . . . . . . . . . . . . . . .37
Fig. 21. Uranium concentrationprofileof the extraction/scrubcolumn. . . . . . . . . . . . . . . 39
Fig. 22. Uranium concentrationproffleof the strippingcolumn. . . . . . . . . . . . . . . . . . .40
Fig. 23, A hypotheticalconcentrationprofdeof uraniumconcentrations. . . . . . . . . . . . . .41
Fig. 24. Estimatedprofile-piecewise linear approximation. . . . . . . . . . . . . . . . . . . . .42
Fig, 25. Estimated profile-regression methods. . . . . . . . . . . . . . . . . . . . . . . . . . 0 043
Fig. 26. Estimated protile-Burkhart model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
Fig. 27. Estimatedprofile-regression methods. . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Fig. 28. Estimatedprotile-Burkhart model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48
Fig. 29. Estimatedprofile-regression methods. . . . . . . . . . . . . . . . . . . . . . . . . . . .48
Fig. 30. Estimatedprotile-Burkhart model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Fig. 31. Estimatedprofile-regression methods. . . . . . . . . . . . . . . . . . . . . . . . 0 . . .49
 Fig. 32. Estimated profile-Burkhart model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
Fig. 33. An isometricviewof the precipitatorduring solutiontransfer. . . . . . . . . . . . . . . 52
Fig. 34. An isometricviewof the precipitatorduringammonia addition. . . . . . . . . . . . . . 52
 Fig. 35. Detector assemblyand its pedestal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
 Fig. 36. Detector positioningin front of the precipitatorfor measurementsA and B. . . . . . . . 55

                                                                                                                   xi
                                                   FIGURES (cent)


       Fig. 37.   DifferentprofdesofADUholdup alongthe precipitatorcolumn. . . . . . . . . . . . . . 58
       Fig. 38.   A comparisonofinventory differenceswith NDA-measuredtotal holdup. . , . . . . . .59
       Fig, 39.   Linear regressionfit to calcinerdata, . . . . . . . . , . , . . , . , . . . . . . . . , . . . 613
       Fig. 40.   Applicationof Kalman filterto the feed dissolverdata. . . . . , . . . . . . . . . . . . . 61
       Fig. 41.   Applicationof Kalman falterto filterfunnelsdata. . . . . . . . . , . . . . . . . . . . . . 62
       Fig. 42.   Changepointmodelfor the calcinerdata. . . . . . . . . . . . . . . . , . . . . . . . . . .42
       Fig. 43.   Measurementhistory of holdup in the precipitator, , . . . . , . , . . . . , . , . . . . . 65
       Fig. 44.   A smooth curve superimposedon early portionsof the precipitatordata, . , . . . . , .66
       Fig. 45.   Applicationof Kalman filterto steady-stateportion of precipitatordata. . . . . . . . . 67
       Fig. 46.   An isometricviewof the stainlesssteelloop for uranylnitrate solution. , . . . . . . . . 68
       Fig. 47.   An isometricviewof the CPVC loop for uranylfluoridesolution. . . , . . . . . . . . . 68
       Fig. 48.   ShieldedNaI(Tl) detector mounted on a long arm with a designedcapabilityto reproduce
                  measurementlocationson the solutionloop. . . , . . . . . . , . . . . . . . , , . . . . , 70
       Fig. 49.   Measurementhistoryand filteredvaluesfor pumps at lowflowrates. . . . . . . . , . . 74
       Fig. 50.   Measurementhistoryand filteredvaluesfor pumps at highflowrates. . . . . . . . . . . 74
       Fig.51.    Measurementhistoryand filteredvaluesfor stainlesssteelunions. . . . . . . . . . . . . 75
       Fig.52.    Measurementhistory and filteredvaluesfor CPVC unions. . . . . . . . . . . . , . . . . 75
       Fig.53.    Measurementhistory and falteredvaluesfor stainlesssteelvalves. . , . . . . . . , . . . 76
       Fig.54.    Measurementhistory and filteredvaluesfor CPVC valves. . . . . . . . . , . . , . . , . 76
       Fi.g.55.   Measurementhistory and filteredvaluesfor stainlesssteelpipes, . . . . . . . . . . . . . 77
       Fig.56.    Measurementhistory and filteredvaluesfor CPVC pipes. . . . . . . . . . . . . . . . . . 77
       Fig.57.    Measurementhistory and filteredvaluesfor stainlesssteelelbows. . . . . . . . . . . . . 78
       Fig.58.    Measurementhistoryandfilteredvaluesfor CPVC elbows. . . . . . . . . . . . . . . . . 78
       Fig.59.    Measurementhistoryand filteredvaluesfor stainlesssteeltees. . . . . . . . . . . . . , . 79
       Fig.60.    Measurementhistoryand filteredvaluesfor CPVC tees. . . . . . . . . . . . . . . . . . 79
      Fig. A-l.                                                    and                       and
                  A combinationof the gamma-spectraof 232Th its daughters,23SU, the tracer nuclide
                  9sZr-Nb0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
      Fig. A-2. A combinationof the gamma-spectraof natural and/or low-enricheduranium, 23SU, nd              a
                               SC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
                tracer nuclide46




xii
                      ESTIMATION METHODS FOR PROCESS HOLDUP
                           OF SPECIAL NUCLEAR MATERIALS

                                                by

                          K. K. S. Pillay,R. R. Picard, and R. S. Marshall


                                           ABSTRACT

           The US Nuclear Regulatory Commissionsponsored a research study at the Los
        Alamos National Laboratory to explore the possibilitiesof developing statistical
        estimationmethodsfor materialsholdupat highlyenricheduranium(HEU)-processing
        facilities.Attemptsat usinghistoricalholdupdata fromprocessingfacilitiesand selected
        holdupmeasurementsat two operatingfacilities   confirmedthe needfor high-quality data
        and reasonable control over process parameters in developingstatistical models for
        holdup estimations. A major effort was therefore directed at conducting large-scale
        experimentsto demonstratethe value of statisticalestimationmodelsfrom experimen-
        tally measured data of good quality.Usingdata from these experiments,we developed
        statisticalmodelsto estimateresidualinventoriesof uraniumin largeprocessequipment
        and facilities.Someof the importantfindingsof this investigationare the following:
        q Predictionmodelsfor the residualholdup of specialnuclear material(SNM)can be

           developedfrom good-qualityhistoricaldata on holdup.
                                                                                      s
        q Holdupdata from severalof the equipmentusedat HEU-processingfacilities, uch as

           air filters,ductwork,calciners,dissolvers,pumps,pipes,and pipefittings,readilylend
           themselvesto statisticalmodelingof holdup.
        q Holdup profilesof process equipmentsuch as gloveboxes,precipitators,and rotary

           drum filterscan change with time; therefore,good estimationof residualinventories
           in these types of equipmentrequiresseveralmeasurementsat the time of inventory.
        q Althoughmeasurementof residualholdupof SNM in large facilitiesis a challenging

           task, reasonableestimatesof the hiddeninventoriesof holdupto meetthe regulatory
           requirementscan be accomplishedthrougha combinationof goodmeasurementsand
           the use of statisticalmodels.




1. INTRODUCTION

  One of the basicelementsof a systemfor nuclearmaterialsafeguardsis materialsaccountability,which
includesmeasurement,accounting, and procedures designedto provide an accurate knowledgeof the
quantities and dispositionof materials. Section 70.51 of Title 10 of the Code of Federal Regulations
requires,in part, that certain licenseesof specialnuclear materials(SNM) conduct at specifiedintervals
physicalinventoriesof SNM in their possessionunder the license.The accumulationof SNM in process
equipment as hidden inventoriesin the form of residual holdup followingshutdown, draindown, and
    cleanout generally has adverse effects on the quality of physical inventoriesand materials control
    programs. Residualholdupis characterizedby the materialsthat are difficultto locate, sample,identify,
    analyze.and quantify.RegulatoryGuide 5.37,“In-SituAssay of EnrichedUraniumHoldup,”definesthe
    residual holdup of enriched uranium as the inventory component remaining in and about process
    equipmentand handlingareas after those collectionareas have been prepared for inventory.This in situ
    assay guide describesmethods to ensure that a measured valueof residualholdup is includedin each
    materialsbalance.Similarly,RegulatoryGuide5.23 providesguidancefor the assay of residualplutonium
    in processingfacilities.These two regulatoryguides,issued in 1974,are beingrevisedto reflectpresent
    knowledgeon holdupestimationand newrequirementsof materialsaccountability.
       Materials generally accumulate in cracks, pores, and zones of poor circulation within and around
    process equipment. Some processes lead to the accumulationof sizable and sometimescontinually
                                                       f
    increasingamounts of SNM in difllcult-to-recover orm. The walls of the process vessels,plumbing,
    ductwork, glove boxes, and filters often become coated with SNM during materials processing.In
    addition,SNM may chemicallyinteract with the componentsof the processequipment,causinganother
    form of residual holdup.The absolute amount of SNM in residual holdup must be small for efficient
                                                                                                    i
    processingand hazards control.However,in practice,thetotal amountof SNM holdupis significant n the
    contextof the plant inventorydifference.This pointsto the need for better designof processingfacilities
    and improvedmethodsof holdupestimation.


    A. Surveyof PresentKnowledge

      The identificationof the process holdup of fissionablematerials is important not only to materials
    accountabilitybut also to processsafety.Currentregulatorypracticesto preventthediversionof SNM are
    based on the calculationof inventorydifferencesand their standard deviations.Reliablemeasurements
    and estimates of inventoriesare essentialto this regulatory process. The role of hidden inventories,or
    residualholdup,as a problemarea in nuclearmaterialsafeguardswas recognizedveryearly in attemptsto
    establisheffectivesafeguardssystemsin the US.1
       For holdup measurements, in situ assay techniques are preferable to process-disruptiveand time-
    consumingcleanoutmeasurements.The generalprinciplesof thesenondestructiveradiationmeasurement
    techniquesare wellunderstood,and their applicationsto safeguardsmeasurementsare describedin detail
    in several publications generally available to the nuclear material safeguards community. 3 Assay
                                                                                                  “
    proceduresacceptableto regulatorystaff are detailedin regulatoryguidesfor the measurementof uranium
    and plutonium.”sAccuraciesin holdupmeasurementsare generallypoor6,7 because of complexities ‘he    ‘f
    residual depositionpattern and the geometriesof the facilities.There have been suggestionsto avoid
                                                  c
    obviousbias in standards and facility-specific alibrationprocedures.a-ll
       Holdup can be measured by neutron and/or gamma-ray measurements.12’13         Generally,gamma-ray
    techniquesare used becauseof the ready availabilityof the instrumentationand the easeof measurement.
    When attenuation of gamma radiation and geometry become dominant factors, passive neutron
    measurementsare attempted.14Also, a noninvasive     method15 employinga cOCo   gamma-raytransmission
    techniquehas been employedin the determinationof uraniumin a centrifugeplant dump trap.
       The recognitionof the difficultiesassociated with the estimation of process holdup is reflected in
    proposals to use secondary methods of measurement.       12,16-19Design considerations for fiiCilhk tO
    minimizeholdup have been publishedin a regulatory guide     20 t. meet safety requirementsand to ease

    holdupestimationproblems.In the past, there have been attemptsto developestimatesof the contentsof
    process vesselswith the help of elaborate computer programs using previousinventorymeasurements,
    operatingdata, and on-lineprocessmeasurements. These efforts, still in early stagesOfdevelopment,
                                                       21-23

    are intendedto be specificto unit operations.



2
B, Backgroundto This Investigation

   ,4s a resultof the stringentrequirementsfor the timelydetectionof the lossesof SNM and in recognition
               of
of difficulties measuringprocess holdup,the US Nuclear RegulatoryCommission(NRC) initiateda
researchprogram at Los AlamosNationalLaboratoryto evaluatethe use of statisticalmodelsto estimate
the holdup of highly enriched uranium (HEU) at processing facilities.Originally,models were to be
det’elopedusing historicalprocess measurementdata. Holdup problemsof HEU in processingfacilities
and scrap recoveryoperationswerereviewedwith severalfacilityoperators,and an attemptwas madeto
use availableholdup data for developingestimationmodels.The limitedavailabilityof usefuldata and
theirlargeuncertaintiesmadethis a futileeffort.The nextstep was to initiatea seriesof measurementsat a
fewlocationsin threeprocessingfacilitieswithoutinterferingwith normalplant operationand to use these
data for estimationmodels.Althoughthis efforthad limitedsuccess,the problemsassociatedwith holdup
measurementsand the quality of data required for estimation models became more evident.It was
recognizedthat the developmentof statisticalestimationmodelshad to be precededby good measure-
ments,preferablywith controlledprocess parameters. As a result, the program objectivewas redirected
to~’ard designing and performing several large-scale experiments to establish reliable relationships
between materialsthroughput and residualholdup.This report highlightsthese experimentalstudiesof
holdupmeasurementand estimationmodeldevelopmentwith a briefreviewof the holdupmeasurements
conducted at processing facilities and a discussion of the potential values and limitations of such
                for
meiisurements the predictionof residualinventoriesof SNM at processingfacilities.


C. This Report

  This final project report includessummariesof varioustopical and status reports submittedto NRC
                         d
duringthis investigation, etailsof the controlledexperimentsto gatherdata, and the useof thesedata for
developingholdup estimators. Section11summarizesthe effortsto gather holdup data from processing
facilitiesand the potentialvalueof these nondisruptivemeasurementsfor developingestimationmodels.
SectionsIII-VI summarizethe controlledexperimentsto gather highlyreliabledata on holdupand the use
of these data for developingpredictionmodelsof holdup.Section VII is a detaileddiscussionof all the
results and the significanceof the major findingsof this study. A justificationof the use of tracers to
measureholdupof uraniumduringsomeof the experimentalstudies,with adequatedetailson the general
principlesof tracer applications,are presentedin AppendixA. AppendixB providessome introductory
informationregardingthe various statisticaltechniquesemployedin developingholdupestimatorsfrom
experimentaldata. Detailedresultsof controlledexperimentson holdupstudiesare presentedin Appendix
C with summariesand illustrationsin the individualsectionson experimentalstudies.Someof the results
gathered during our search for holdup data from process facilitiesare not included because of the
proprietarynature of the information.
  The findingsof this investigationfurther confirm the difficultiesassociated with estimatingresidual
SNM in processing facilities.However,the task of estimatingholdup inventoriescan be made easier
through the developmentof process- and plant-specificestimation models. This approach to holdup
estimationis less disruptiveto plant operations,and the measurementsrequired to develop reasonable
estimatesof the hiddeninventoriescan be carried out with minimaldisruptionsin productionschedules.


H. HOLDUP MEASUREMENTSAT PROCESSING FACILITIES

  This section summarizesthe important accomplishmentsof the attempts to measure and model the
holdup of SNM in selectedequipmentat three processingfacilities.In recognitionof the limitationsof
historicaldata on holdup availablefrom HEU-processingfacilities,an attempt was made to perform

                                                                                                           3
    nondestructiveassay (NDA) measurementson selectedequipmentto gather data and to determinethe
    feasibilityof developingestimationmodelsof holdupfromthese carefullydesignedmeasurements.These
    measurementswere conductedat TA-55 (the PlutoniumProcessingFacilityat Los Alamos)and TA-21
    (the HEU Scrap Recovery Facility at Los Alamos).In addition,some of the historicaldata on uranium
    holdup in ducts at the high-temperaturegas-cooledreactor (HTGR) Fuel Fabrication Facility of GA
                    I
    Technologies, nc., at San Diego,California,wereof value.Althoughthe measurementsweremadeon air
    filters,air ducts, conversioncalciners,and someprecipitationand filtrationequipment,the measurements
    on air filterswere particularlyusefulfor developingdynamic estimationmodels.The data obtainedfrom
    other equipmentshowed stable or erratic holdupor had seriouslimitationsbecauseof high background
    levelsin the areas of measurementand the apparentlack of stabilityin the holdupduringthe measurement.
    The holdup measurementswere conducted for continuousperiodsrangingfrom 6 months to 1 yr. It is
    significantthat measurements were made during normal process operations and that there was no
    additional control over the operation of these facilitiesfor the purposes of holdup measurements.
    Measurementswere made at the convenienceof the facilityoperatorswith minimalinterferencewith their
    productionschedules.


    A. MeasurementTechniques

                                                                p
       The holdupmeasurementsof plutoniumon a high-efficiency articulateair (HEPA) filterat TA-55 were
    performedusinga shieldedand collimatedNaI(Tl) detectorinstalledon top of the glovebox about 18cm
    from the filter.A multichannelanalyzer system was used to scan the gamma spectrum,and the 320- to
    470-keVregion was integratedto determinethe holdup on this filter.Standards used in calibratingthis
    detector system were fabricatedto resemblethe filterbeingmeasuredby preparingstandards on HEPA
    filters with known amounts of PuOZ dispersed on the filter medium. Transmission and attenuation
    correctionswere determinedusinga thin source of PuOZ.
       Allthe holdupmeasurementsconductedat TA-21 wereperformedusinga two-channelstabilizedassay
                                                                A
    meter (SAM-2, manufactured by Eberline Corp.) and a 241 m-doped NaI(Tl) detector shieldedand
    collimatedwith lead.The filterswere measuredin-placein steelhousingson top of the gloveboxes.Thin
    foilsourcesof 235U  wereused for detectorcalibrationand attenuationcorrections.
       Most of the holdup measurementsof uranium in conversion calciners at TA-21 were done using
    gamma-assaytechniqueswith a SAM-2unit.Holdupof uraniumin eightbatch calciners—fourofthemin
    use for 8 yr and the other four in use for 28 yr—were measured for -15 months. Several sets of
                                                 d
    measurements,usingboth thermoluminescent osimeters(TLDs) and a NaI(Tl)detector,weremadewhen
    the furnaces were cooled down between process batches. The shieldedNaI(Tl) detector with a wide
    viewinganglewas reproduciblyplacedin front ofthe entranceto the calciners,whichwerelocatedin glove
                                                                           d
    boxes,to make periodicmeasurementsof holdup.For thermoluminescent osimetry,pairs of TLDs were
    placed at three locationsinsidethe calciner.The measurementswere made usingCaFz (Mn) bulb TLDs
    and a Model 2810 TLD reader, manufacturedby VictoreenInstruments.The TLDs were placedin the
    calcinersat room temperaturefor 2-4 days and were read within24 h after exposureto limitthe loss of
                            B
    stored energy to < IVO. ecauseof the nonuniformdistributionof holdup withinthe calciners,the TLD
    data were much more readily normalized than the NaI(Tl)-detector-measured     data. The distribution
    profilesof the uraniumholdupinsidethe calcinerswere determinedusinga very small,highlycollimated
    NaI(Tl)interiorsurveyprobe.
       The holdupmeasurementdata gatheredfromthe HTGR FuelFabricationFacilityof GA Technologies,
    Inc., covered 18 months,althoughnot all facilitieswerein continuoususe duringthis period.These were
    bimonthlyinventoryrecords (historicaldata). Holdup measurementson the facilityexhaustduct system
    wereexaminedas part of this effort.The NDA measurementsof holdupin the duct systemused SAM-2
    gamma-assayinstrumentation.


4
B. Holdup MeasurementResults

   1. PlutoniumFacility Filter Holdup. The holdup measurementdata from the air filter at TA-55 are
probablythe best on air filterholdupobtainedduring these measurements.This is due to the locationof
this filter away from high-backgroundareas; the f~ed, shieldedpositionof the detector; and the use of
better calibrationstandards and instrumentationfor routinemeasurements.This is further demonstrated
by the confirmatorymeasurementson the filtersat the end of the experiment.The air filterremovedwas
measured using a neutron coincidencecounter to determine the plutonium content. The coincidence
counter measurementwas within8% of the in-placeNDA estimatesof the holdupof plutonium.Table I
liststhe holdupmeasurementvaluesand processthroughputdata correspondingto -13 months.

   2. Uranium Scrap Recovery Facility Air Filter Holdup. Exhaust air filters from three gloveboxes
(DB-1, DB-24, and DB-30) at TA-21 were periodicallymeasuredto determineuranium holdup and its
variationwiththroughput(TableII). Thesedata indicatethat the firstthree measurementsfor filterDB-24
wereerratic. This was due to the very high backgroundvaluesin that locationand the very smallamount
of uranium on the filter.The data from the other two filtersappear to be reasonably wellbehaved.An
estimateof the standard error applicableto all the holdupvaluesin Table II is 0.2 g of 23SU.

   3. Uranium Holdup in Batch Calciners.The holdup measurementson the calcinerswere done at the
convenienceof the facilityoperators to minimizeprocessdisruptions.Also,the routineproceduresat the
                                    for
facilitywerenot alteredsignificantly thesemeasurements.Theseproceduresincludedperiodiccleanout
of the calciner with a brush or vacuum cleaner to remove obviousspillsand residuals.These activities
made it very difficultto gather holdup data that could be correlated with throughput of uranium in the
calciners.
   Table III summarizesa significantpart of the calcinerholdupdata. However,thesedata cannotbe used
for accurate predictionoffutureholdupbecauseof largevariationsin the use pattern and cleanoutregimen
of the calcinersduringthese measurements.

   4. Precipitatorand Rotating Drum Filter Holdup. A precipitationand fdtrationsystemat TA-21 was
measuredfor uraniumholdupduringroutineuse.The equipmentconsistedoftwo stainlesssteeltanks(one
of which was a precipitationvesselwith a mechanicalstirrer)and a rotary drum falter.The filtermedium
was a strip of polypropylenefabric placed around the drum. Uranium from the scrap recoverysolutionis
                                               at
precipitatedas uranium peroxide(U04.XHZO) a pH of w2.Ousinghydrogenperoxideas a precipitant
and NH40H as a buffer.The slurry is sucked onto the filter strip to separate the precipitateduranium.
When the moist cake deposit reaches a thicknessof -3 mm, it is scraped into a collectionboat usinga
doctor blade. Under normal conditions, an 8-kg batch can be precipitated and filtered within 6 h.
However,if precipitationdoes not proceed smoothly,the process is terminated,the falterdrum is hand-
scraped, the drum is pickled in 1O-MHN03, and the process is continued the next day. Because of
differingend-of-shiftconditions,the precipitationtanks and the rotary drum filtercan havevery different
end-of-shifturaniumholdups.Six measurementsmade duringa 6-month period indicatethat the end-of-
shift holdup can vary from z 10 g for normal runs to x150 g for the problematicprecipitations,those in
whichthe filterswere hand-scrapedrather than pickled.

                                                                                  I
   5. Uranium Holdup in Air Ducts. Extensivemeasurementsat GA Technologies, nc., fromNovember
1979through May 1981 on fiveduct systemsshowedno discerniblechange in the holdup.It should be
added that not all the duct systemswere in continuoususe during the period becauseof the production
schedulefor variousoperationsat this facility.The ducts weremeasuredbetweenthe gloveboxesserviced
and the first filter.Figure 1 showsthe averageholdupin four of the fiveduct systemsthat were in use for
at least 6 monthsduringthese measurements.
    TABLE I. Holdup of Plutoniumon a GloveBoxAir Filter
       Throughput      Holdup     Throughput     Holdup
          (kg)           (g)         (kg)          (6)
           3.3           0.6        148.1         53.5
          12.7           4.0        151.8         54.7
          17.4           3.9        151.8         54.9
          17.4           3.8        151.8         56.0
          18.9           3.9        155.4         57.6
          23.7           5.3        159.2         59.6
          25.3           5.4        165.0         61.2
          26.2           6.6        166.9         62.3
          30.9           6.6        166.9         63.2
          30.9           6.7        170.3         64.1
          32.6           6.9        170.3         64,1
          38.3           8.1        174.3         65.8
          38.3           800        176.1         65.8
          59.5          14.7        176.1         67.5
          64.3          16.7        176.1         68.0
          71.4          18.0        185.4         68.0
          73.3          17.0        194.0         69.9
          77.0          19.2        198.3         70.4
          85.4         24.1         198.3         71.7
         113.3         35.1         202.7         73.9
         113.3         35.0         206.2         73,9
         113.3         35.2         211.5         76.0
         116.9         35.9         211.5         76.2
         117.8         37.3         211.5         76.5
         122.1         39.0         215.1         76.5
         125.5         42.3         215.1         76,25
         127.0         42.4         235.3         87.27
         127.0         42.7         238.9         88,7
         129.2         42.9         242.8         89.5
         132.8         43.0         244.6         91.0
         132.8         44.0         244.6         91.3
         136.6         45.1         255.5         91.3
         142.3         48.7         280.6         98.9
         142.3         49.9         287.2        100.8
         144.1         52.3




6
       TABLE IL       Holdup of Uranium on Exhaust Air Filters at TA-21


         Date of                  DB-1                      DB-24                       DB-30
        Measurement         t’            h’        t’           h’              t’         h’
          8/11/81          0.1           1.3     0.0               1.7          0.0           1.6
                                         0.9                       2.0                        0.6
          9/02/8]          3.5           2.9     0.6               2.2          4.7           0.5
                                                                                              0.5
          9/22/81          7.0           3.0        1.2            3.1          5.6         2.1,2.5
                                                                                              2.5
          11/05/81         15.0          3.5     2.5              1.1,1.6       9.3           3.7
                                                                  1.2,0.8                     3.8
          1l/25/81         18.0          3.7     3.1               0.7          10.0          4.0
                                                                   1.1                        4.0
         12/23/81          22.0          3.5     3.8               1.4          12.0          5.1
                                                                   2.4                        4.6
          2/24/82          32.0          4.9     5.6               1.3          18.0          5.3
                                                                   1.4                        5.7
          4/01/82          39.0          5.4             tilt-w rsplaced        23.0           6.3
                                                                                               5.9
          6/15/82          50.0          5.8        --              --                -falterreplaced
                                     i           ofurenium,snd h denotesholdupin gmsrrs
       “Heret denotesprocessthroughput n kilograms
       of uranium.




                                                          Profiles
                         Holdupfor CslcinersWeighted Mnterisl
TABLEIII. Grsms of Uranhms                         by
                 Aug.27, 8ept.23, Get.22, Gc.L26, Nov.5, Nov.1O, Dec.22, Mu.15, April 30,
Celciner Probs      1981    1981     1981      1981         1981         1981   1981       1982         1982

         Nat         11      12          13    13            13          12      11         11          11
  35     TLD         14                        16                        14      20         20          19

         Nd          33      37          37    40            39          36      36         38          32
  34     TLD 46                                47                        47     47          51          36

         Nd          41      47          44    46            45          39      42         41          34
  33     TLD         61                        47                        43      49         51          59

         Nel         30      35          35    35            37          31     33          35          28
  32     TLD         33                        30                        28     41          39          43


         NaI         87     119      132       123          116          117    115        115          105
   5     TLD        139                        92                        78     118         108         114

         Nml         108    157      1s4       146          141          12A    98          103         82
   4     TLD        123                        93                        99     82          82          83

         Nd         113     166      152       136          132          132    126        138          121
   3     TLD        126                        103                       96     118        118          118


         Nd         130     175      165       156          145          155     -–        156          141
   2     TLD        162                        149                       131    204        167          160




                                                                                                               7
                                                        URANIUM HOLDUP

                    “’~

                    350

                                  0                                                0
                    300
              z
              IL                                                                                fi
                                                                                                P
              0     250                            o
               0)
                                                                   o


              %     200
              a                                                                                        u
              &
              x     150

                    100

                     50 J         I         i       I       1       1       I       1       I          I
                                  J       A        s       o       N       D               F          M     A
                                         1980                                       1981
                                                        MEASUREMENT DATE                             Lot A!arnos
                          Fig.1. Total   holdup of uranium in four duct systems at GA Technologies, Inc.




    C. Modeling

      An air filterat TA-55 was monitoredperiodicallyfor 13 months.The results are listedin Table I and
    plottedin Fig. 2. A clear relationshipbetweenmeasuredholdupand throughputexistsand can be exploited
    for predictivepurposes.That is, giventhe measurementhistoryof the filterup to a particulartime,holdup
    estimatesfor futuretimescan be derived.
       For these data, a smoothcurveis derivedthat estimatesthe functionalrelationshipbetweenholdupand
    throughputunder the existingoperatingconditions.The curve, superimposedon Fig. 2, is

         = 0.2845t+ 0.0003974t2,
      fi(t)                                                                                                        (1)

    where fi(t) is the estimated filter holdup (in grams of plutonium)when the process throughput is t
    kilograms.The coefficients0.2845 and 0.0003974are producedby a least squaresfit to all but the final
    three points.The presenceof a quadratic term in Eq. (1) reflectsa nonlinearityin the accumulationof
    material;that is,holdupon the filterdoesnot simplyincreaseproportionallyto throughput.Data fromthe
    filtersused in the dust-generationexperiments(Sec.III) exhibitsimilarnonlinearbehavior.
       Despitethe good overallfit of the model[Eq. (1)]to the data, carefulinspectionof Fig.2 indicatesa few
    minor “discontinuities.”For example,at -235 kg of throughput,over 200 archive samplesof 50 g of
    PuOZeach wereopenedand pouredinto a singlecontainer,therebygeneratinga slightlyincreasedamount
    of dust. The final three measurements,coming after 250 kg of throughput, represent blending and
    packagingoperations,which are relativelydustfree compared with blendingand screening.The minor
    inadequaciesof the fitted model for this filter are primarily the consequenceof operationalchanges.
                             to
    Becauseit is impossible maintainexactlythe sameprocessconditionsovertime,somejudgmentmaybe
    requiredto determinewhethera modeldevelopedin one contextappliesin another.In the case at hand, it
                                                                       is
    seems clear that the holdup generatedduring blending/screening markedlydifferentfrom that during
    blending/packaging.
8
                  120                I            I            1             I            I            /




                  100
                                                                                              o


             2     80
             k
                   60

             ;
             o
             I     40


                   20

                                     I            I             I
                    0                                                        I            I

                        o           50           100          150          200          250            300
                                                  THROUGHPUT(kg OF P@
                   Fig. 2. Measurement history of the holdup of plutonium on an air filter at TA-55.



   Central to good predictabilityare the stable(consistent)operationof the glovebox and the highquality
of’measurement data. These prerequisitesmay not be achievedfor all operations at all facilities,and
modelingefforts wouldsufferas a result.For example,if a holdupmodelis to be developedsolelyon the
basisof throughput,it is importantto holdconstantallotherfactorsthat affectthe accumulationof holdup
(such as the levelof airflowand the type of materialhandledfor the TA-55 fiiter).If such relevantfactors
are variedovertimeand are unmeasured,they cannot be accountedfor in a model.For the filterat TA-55,
the processoperationremainedrelativelystable and facilitatedusefulmodeling.
   Also contributingto successfulmodelinghere is the highqualityof data. Large measurementerrors can
easily obscure the nature of material depositionand make diflicultthe extraction of a model. These
           can                                                  A
difficulties be compoundedif data are obtainedinfrequently. s the accurate accountabilityof holdup
has not often been a high priority at processingfacilitiesin the past and as it is nontrivialto overcome
some of the measurementproblems,historicaldata are often of limitedvalue.
   The measurementhistoriesfor three filtersat TA-21 are plotted in Figs. 3-5. As describedpreviously,
uranium holdup on these filters behaved somewhat differentlyfrom the holdup on filters at TA-55.
Consider the filter labeled DB-1. Following two unusual measured values at zero throughput, the
accumulationon this filter was approximatelylinear during the observation.In contrast to the filterat
T.A-55,the initial measurementshere were expected to be nonzero because of residualmaterial in the
housinginto whichthe clean filterwas inserted;however,no definitive   explanationexistsof the (apparent)
large increasein holdupover the first 3,5 kg of throughput.It is possiblethat the first two measurements
werepoor, but there is no firm evidenceof this.
   The rest of the data are welltit by the model

  Ii(t)= 2.496+ 0.068t .                                                                                     (2)
     7 I              I            I           I            I              I




     0                I            I           I           I              I

         0           10          20           30           40             50      60
                                   THROUGHPUT(kg OF U)

         Fig. 3. Measurementhistoryof the holdupof uraniumon air filter DB-1.




                                                                      I

         o                5            10             15             20           25
                                           (kg
                                   THROUGHPUT OF U)

          Fig. 4, Measurementhistory of the holdupof uraniumon air falterDB-30.




10
                                       0




                                                                        0
                             0




                                                       0
                                                                        u
                                                      o
                                                      0           u




                                   I            I             I             I           1


                     0             1            2            3              4           5        6
                                                        (kg
                                                THROUGHPW OF U)

                     Fig. S. Measurement history of the holdup of uranium on air falter DB-24.



There is no detectablecurvature here in contrast to the previousplutoniumblending/screening   example
and to the filters used in the dust-generationexperiments(see Sec. III). Use of Eq. (2) for predictive
                                                           of
purposesis straightforward.The futurethroughputvaluetO interestis substitutedintoEq. (2)and h(%)is
                                             i
calculated.The standard deviationof fi(tO)s acquiredfollowingstandard regressiontheory and can be
us,~dfor accountabilitypurposes.
   When modelssuch as Eq. (2) are usedto “extrapolate”outsidethe rangeof the measurementdata, there
are two important considerationsto keep in mind. First, it is implicitlyassumed that the nature of the
process operation willremain reasonablyconstant. As seen for the TA-55 filter,the modelconstructed
based on the blending/screening  data did poorly in explainingthe blending/packagingresults.The second
considerationinvolvesthe nature of the standard deviationof fi(tO), whichincreasesas a functionof ~. In
other words,predictionof holdupa day in advanceis likelyto be more accuratethan predictionof holdup
a month in advance.Althoughit is certainlypossibleto substituteinto Eq. (2) valuesoft wellbeyondthe
range of the existingdata, the resulting estimates would have very large standard deviations.Thus,
extrapolated values should be interpreted with caution. Maintaininggood accountabilityrequires that
measurements be obtained periodicallyand used to update the fitted model. The frequency of data
collectionthus dependson the desiredaccuracy of estimation.
                                                                                         i
   The procedurefor updatingthe modelis a simpleone. When a new measurementm(tO)s obtainedat
               i                                     b
throughputtO, t is comparedwithits prediction6(tO) asedonlyon earlierdata. The differencem(tJ - F(%)
should fall within a prescribed range—for example, plus or minus three standard deviationsof the
difference.Indeed,controlcharts of such quantitiesare usefulin evaluatingmodelperformance.If m(tO)    -
     is
fi(tO) sufficientlysmall,then m(b) is addedto the previousdata and parametersof the modelre-estimated
                                                          –      i
based on all availableinformation.If the differencem(tO) fi(tO)s outsideits prescribedlimits,this is an
inclinationthat the model may have broken down or, perhaps, that the new measurementm(tO)is an
outlier;in eithercase, furtherinvestigationis suggested.




                                                                                                          11
        The updatingprocedureworks quite wellfor short-termpredictionand testing.For example,givena
     modelbased on present and past data, predictedvaluesfi(t)and their associatedstandard deviationscan
     be computed for values of t in the near future. The predictionscan then be combined with other
     informationto assess potentialloss in the short term, When the next inventorytakes place and another
     holdupmeasurementis made, the modelis updated as described,and short-termpredictionscan then be
     made usingthe updatedmodel,
        Considernow the DB-30 filter(Fig, 4). It appearsthat this filteris approachinga pluggedstate by the
     end of the observationperiod.The materialbeingprocessedhere is nominally2.6 wt~o231J,so 6 g of 235U
     representsa total depositionon the filterof wellover 200 g. By contrast,the incineratorash on the DB-30
                                                    are
     filteris roughly 15 wt% 235U, nd 6 g of *JSU equivalentto a 40-g accumulation.When an air filter
                                     a
     becomescompletelyplugged,airflowthrough it ceases and essentiallyno materialis transportedonto it,
     This phenomenonis reflectedin the measurementhistory (Fig. 4). At such a point, it is necessary to
     replacethe filter.
        Over the range of the data, the second-ordermodel

       fi(t)= 0.496 + 0.427t- 0.008t2                                                                    (3)

     captures the increasingdeposition.The interceptterm, 0.496, in Eq, (3) reflectsthe presenceof residual
     material in the housingat the time of filterinstallation.If there were no initialmaterial,a model“forced
     throughthe origin”wouldbe appropriate.The concaveshapeof the fittedcurveis the consequenceof the
     pluggingand is unique among the filters analyzed during this investigation.Such shapes can also be
                                                                       that
     describedby morecomplexmodelssuch as isotonicregressions24 imposemonotonicityconstraintson
     h(t). Certain types of mixturemodelsmightalso be of use. In any case, it seemsclear that the amountof
     holdupon the filteris rapidlyapproachinga limit.
        Finally,considerthe measurementhistoryof the DB-24filter(Fig. 5).Thesedata are quiteerratic, not
                                                f
     exhibitingsufficienttemporalcontinuity2s or modeling.Very high backgroundlevels(or poor signal-to-
     noiseratio) made the nondestructivemeasurementof the relativelysmall quantitiesof materialdiftlcult.
     Lacking informationfrom externalsources,such as from analysesof other filters“known” to behavein
     the samefashionas this one,there is littleon whichto placeconfidencein a modelwhenthe signal-to-noise
     ratio is very low.
        The measurementof the conversioncalcinersat TA-21 provided much usefulinformation,and the
     controlledexperiment(Sec.V)on calcinerholdupbenefitedas a result.However,the data derivedwerenot
     amenable to modelingfor reasons described below. Basically,the particular constraints imposed by
     processingoperationsprohibitedconstructionof a modelcapturingallthe relevantfactorsknownto affect
     the holdup.
        An initialditlicultyarose in attemptingto obtain a singleNDA measurementof each calciner,that of
     overcomingthe effects of nonuniformdeposition.To some extent, this difilcultyexistswith respect to
     nondestructivemeasurementof many other objects.The nonuniformdepositionwas causedprimarilyby
     the nature of the construction,use, and maintenanceof the equipmentand was the largestsinglesourceof
     error for thesemeasurements.
       There are alternativeapproachesto overcomethe effectsof nonuniformdeposition.One is to beginby
                                                 w
     carefullycharacterizingthe nonuniformity, hichcan be doneby obtainingmeasurements          fromindividual
     locations.For example,TLDs couldbe insertedat variousplaceswithinthe calcinerto providefor such a
     characterization.A future single-measurement   count rate can then be convertedto quantitiesof material
     after properly accountingfor the holdup profile.Of course, such a measurementprocedure implicitly
     assumesrelativelylittlechangein the depositionpatternovertime,but fewalternativesexistwhenexternal
     constraints allow for only a singlemeasurement.If severalmeasured values are obtained from distinct
     locations, a more exact profile model can be constructed and more accurate single-measurement
     correctionscan be made. The analysisof the pulse-columndata (Sec. IV) is a good exampleof profile
     estimation.

12
   A final note of interestregardingthe calcinermeasurementsinvolvesthe cleaningof the calciner.For
most processingoperations,a “typical”state of cleanliness    exists.In this case,the calcinerswerebrushed
out after each calcination.Starting October 1981,they were vacuumed after each calcination,and the
material collected was sent to recovery. Obviously, such activities greatly influence the residual
holdup—observedchangesin measuredvaluesover time may reflectmore on the levelsof the cleanout
efforts than on anything else. For example,the scintillationdetector data indicatedthat the calciners
                                                                                          is
tendedto becomecleaneras the vacuumingcontinued.The factor “cleanoutefficiency” quiteditllcultto
quantifyfor incorporationintoa model,and whensuch importantfactorsare allowedto vary considerably
over time,there is littlehopefor successfulmodeling.Such was the case for the calciners.
   Data obtained from fuel fabrication facility ducts at GA Technologies,Inc., where holdup had
accumulated for many years, offered the possibilityof studying the process under near-steady-state
conditions.It was hopedthat changesin holdupover the briefperiodof observation(briefrelativeto duct
lifetime)would be minor and that the effects of other factors—such as duct geometry—couldbe
evaluated.For example,the amount of holdup per unit area of interiorsurface at an elbow mightbe a
predictablemultipleof the amountper unit area for the precedingstraightsegment,
   Unfortunately,it was not possibleto reach substantiveconclusionsregardingtheeffectsof such factors.
Tht major problem lay in the quality of measured values. From counting statistics and replicate
                                                           r
measurements,it was apparent that a low signal-to-noiseatio largelyobscuredthe observationof small
quantitiesof holdup. Unusuallyhigh backgroundlevelsfrom thorium daughtersat the facilitywere the
primary cause, and it was very impracticalto circumventthis difficultythroughthe useof heavyshielding
or l,hroughthe removalof the ducts to a better environmentfor measurement.
   Estimatinggeometricaleffectsfrom the individualduct systems was quite ditlicult.Based on results
                                                              r
frolmareas of larger holdup(and thus better signal-to-noiseatio),the anticipatedconclusionthat elbows
serve as accumulationpoints was clearly substantiated.Making a more definitivestatementto quantify
this effectwouldbe ill-advised becauseof the magnitudesof measurementerrors and, perhaps,becauseof
“interaction” with other relevant factors; that is, the “elbow effect” may not remain constant over all
combinationsof other factors such as duct composition,duct diameter,and type of equipmentserviced.
   Quantificationof other effectsis similarlyprecluded.Though steady-statemodels(Sec. V) might be
used to provide estimates of holdup at individuallocations,it is quite difficultto make comparative
statementsregardingvariousfactors affectingholdup.


111.EXPERIMENTAL STUDY OF URANIUM HOLDUP IN A DUST-GENERATING FACILITY

  The problem of tissile materials accounting in fuel material preparation and fabrication facilitiesis
increasedby the difficultyof accuratelyestimatingthe amountof SNM that is heldup as residualsin glove
boxes, ducting, ventilationfilters,and other processingequipment.The residualholdup associatedwith
dust-generatingoperationscan be a serioussafety problemas wellas a materialsaccountabilityproblem.
The safety problemcan be minimizedby facilitydesignconsiderationsand periodicradiationmonitoring
with appropriate portable instrumentsfollowedby cleanout of areas with large material accumulation
potentials.However,there are no simplenoninvasiveproceduresfor reasonableestimationsof residual
holdupof SNM in gloveboxes,ducts, and ventilationfilters.The recognizedlimitationsof historicaldata
on residual holdup in dust-generatingfacilities have prompted this attempt to perform controlled
experimentsand to developholdupdata as a functionof materialthroughput.




                                                                                                            13


                                                                                                                 I
     A. Facility Description

         An experimentwas designedto generateuraniumholdupdata to examinethe build-upof uraniumdust
      on gloveboxes,exhaustducts, and exhaustair filtersurfacesat the HTGR fuelfabricationfacilityof GA
     Technologies,Inc. This facilitycontainscoated-particleand fuelrod-productionfacilities,scrap recovery
      lines, low-levelcombustibleincinerationequipment,and fuel storage areas. At the time of the holdup
     experiments,this plant was processing only fertile material (thorium). It was, therefore, possible to
     dedicate gloveboxes and duct/filtersystemscontainingfissilematerialand the necessary measurement
     equipmentfor this task.
         The facilityis equippedwith air ducts of three differentdesigns.Many of these ducts are made from
                               g
     round, spiral-lockseam, alvanizedsteel,The ductworkvariesin materialthicknessfrom 1to 2 mm.Also
     usedextensivelythroughoutthe facilityare round polyvinylchloride(PVC)ducts.Theseductshavea wall
     thickness of -6.0 mm with diameters ranging from 10 to 40 cm. In addition, there are spiralwire-
     reinforcedrubber ducts. The spiral-lockseam    ducts use automaticair-control(constantvolume)valvesto
     control airflow.These controllersare generallypresetat 100cfm (2.8 m3/min)and servethe ductsleading
                                                                                     q
     to severalgloveboxes.Smallducts servicingthe gloveboxes,wheresignificant uantitiesof airborneSNM
     are generated,wereequippedwith prefilters.The prefiltersare locatedas closeto the equipmentenclosure
     as possible(1-3 m). Smallducts are combinedinto large ducts that route the exhaust air to a finalfilter
     bank. In this filter bank, the exhaust air passes through 5-cm-thickmedium-efficiency         filters, called
     intermediatefilters,and finallythrough a bank of large HEPA filters.
         A glove box and ventilation system, using materials and designs similar to those used at GA
     Technologies,Inc., for the uranium-and thorium-processing     equipment,was set up to generateuranium
     dust and for in situ holdup measurements.Figure 6 shows a schematicdiagram of the glovebox and
     duct/filtersystem,occupying-6 x 5 x 7 m,
         As shown in the illustration,10-cm-diamductingmade of spiral-lockseamgalvanizedsteelas wellas
     PVC ductingwere used in the constructionof the exhaustair system.Elbowsand tees constructedfrom
     both types of materials were also included.-To facilitate rapid teardown and reconstruction of this
     ventilationsystem,the ductingwas not attachedto the facilitystructurepermanentlybut was heldtogether
     usingrubberjoints and clamps.
         The glovebox (1.5 x 0.9x 1.2m) was locatedso that the ductingcouldbe connectedto existingprefilter
     boxes and airflow controllerswithin the facility(Fig. 6) and to provide easy access for measurement
     equipment.The locationsof 14 background measurementpoints used in the experimentsare detailedin
     Table IV.
         The pretilters are located in steel enclosures,equipped with pressure differentialgauges to monitor
     airflowthrough the filter.The prefiltermediawas a nonwovenglass-fiberfabricsupportedon a wirecloth
     grid, pleated to a 2-in. depth with an “open” rounded pleat edge design,and supportedwithina water-
     resistant paperboard frame. They were medium-efficiency      filters with an efllciencyrating of 92Y0.To
     further capture the SNM in the ventilationsystem,the filtration system used for this experimentwas
     modifiedto accommodatetwo prefilters(shownas upstreamand downstreamfilterson Fig. 6) beforethe
     intermediateand absolutefilters.
         All HEPA absolutefiltersand their associatedventilationmechanismsare locatedcentrallyrather than
     located at or near the equipmentitself.The absolutefilters,rated as 99.97Y0    eflicient,were made of fire-
     retardant particleboard framewith a waterproofglass-matfiltermediaresistantto organicsolvents,acids,
     alkalies,and fire.The absolutefilterwas immediatelyprecededby an “intermediate”filterlocated in the
     HEPA cabinetto extendthe lifeof the HEPA filter.
         A mechanical dust-generatingapparatus, designed and fabricated for this experiment, is shown
     schematicallyin Fig. 7. The dust generator consistedof (1) a deliveryand receivingbottle with funnel
     assembly,(2) a vibrator assemblyto assistuniformmaterialflowfromthe deliveryto the receivingbottle,
     (3) a modifiedbottle cap with adjustableorificefor flowadjustments,and (4) adjustmentfor drop angle
     and height.

14
PVC ELBOW1




                  60 L x 30 Wx 50 cm  J
                 ‘REFILmR
                        (upstream)         TO




                                                              (DOWNSTREAM)
                                                      PREFILTER
               “R ‘NLETF’LTER




                  GLOVE BOX VENTILATION SYSTEM
                         USED FOR HOLDUP
                   GENERATION AND MEASUREMENT
    Fig. 6. An isometric view of the experimental iacility.



 TABLE IV. Locationsof MeasurementPoints
   Measurement            BackgroundMeasurement
     Pointa                      Location
           1              60 cm behindglovebox
          2               60 cm behindglovebox
          3               60 cm to leflof glovebox
          4               60 cm in front of glovebox
          5               60 cm to right of glovebox
           6              45 cm to right of assay point
           7              45 cm to right of assay point
           8              45 cm to right of assay point
           9              30 cm belowassay point
          10              30 cm belowassay point
          11              30 cm belowassay point
          12              30 cm belowassay point
          13              30 cm belowassay point
          14              60 cm to right of prefilter
                          housing
       n      referto pointsmarkedin Fig.6.
  *These umbers
                                                                             15
                          1/2 GAL. PLASTIC
                          DELIVERY BOTTLE


                                            /\?L::::&%k:




                                 J?&
                               CLAMP                  //v

                                                             / /’
                                                                       /




                           &/k
                                                                                        DROPHEIGHT
                                                                                        ADJUSTMENT




                            .- /
                  MODIFIED




                             :
                  BOTTLE                              /:–––
                  CAPWITH                       ,/     (+
                  ORIFICE
                                       ‘$’’::’ 6––::                             (3




                       “%+
                                                     o:             ““           0




                     -00 “BRATOR
                          )-$
                                                           RECEIVING
                                           -FUNNEL
                                                           ASSEMBLY                     — STANO

                                                       GAL.PLASTIC
                                                     1/2
                                                     RECEIVING
                                                             BOTTLE



                                                     BOTTLE
                           /                         HOLOER
                           !
                          t+
                                                                                [
                                                                                —

                                  Fig. 7. A schematicof the dust-generationapparatus.




     B. ExperimentalProcedures

        For the in situ measurementof holdupin the glovebox and ventilationsystem,commerciallyavailable
                                                                    a
     gamma-ray instrumentationINaI(Tl)detectorand single-channel nalyzer]was used.The criticalaspect
     of these measurements,however,is the precisemeasurementof smalldepositionsof uranium(milligram
     quantities)in the system.The estimationof these depositionsby the direct measurementof gamma rays
                         has
     emittedfrom ZSSU seriouslimitationscaused by the low specificactivityof the nuclideand the high
     backgroundlevelsof thoriumdaughterradiationsin the processfacility.

        1. Tracer Application.The sensitivityof such holdup measurementscan be improvedsignificantly   by
     thejudicialincorporation(spiking)of trace levelsof radionuclideswithhighspecificactivityand desirable
     gamma spectral characteristics.The principlesof the uses of tracers and their unique advantages are
     discussedin AppendixA,
       The tracer materialwas prepared by irradiatingseveralsealedquartz capsules,each containing-200
     mg of UjO.s.For experimentsinvolvingincinerator ash, samples of ash materials were irradiated to
     prepare the tracer. The irradiationswere performedin the neutron flux of a TRIGA Mark-F Research
     Reactor Facility,The core positionhad a thermalfluxof-2 x 1013   n/cm2.s,Irradiationtimevariedfrom
     -30 to 60 min dependingon the sample material and the activity desired in the sample.Thus, -lO1s

16
fissionswere inducedin the 200 mg of 95%-enrichedU~O~   sample.This amountsto < 10’5nuclidesof the
tracer 95Zr-95Nbwith an initialactivityof -3 x 107Bq. Followingirradiation,the samplewas left in the
reactor pool for a coolingperiod of *2 weeksto optimizethe relativegamma fluxof the desiredfission
productsbeforebeingused for the experiments.
   The homogenizationor blendingprocedure followingirradiation and cooling was as follows:The
irradiatedsamplesweretransferredto a large mortar and pestlealongwith 150-200g of the bulkmaterial.
The materials were ground together to improveblendingin the bulk material. Two or four irradiated
capsules(400-800mg of UqOaor incineratorash) were blendedto obtain the desiredactivitylevelin the
bulk sample,The ground materialand the bulk materialwere transferredto a V-blenderand blendedfor
20-30 min. At least five grab samples were then obtained from the blended material for homogeneity
determination.Each sample was counted to determineits activity (net counts per minute per gram of
sample) from the desired fission products. The blended material was consideredhomogeneousif the
relativestandard deviationon the averageactivitywas <5%. Standards were prepared from the blended
materialfor daily calibrationof the countingsystem.

   2. Measurements.A 5- x 5-cm NaI(Tl) scintillationdetector (integral assembly)was used with a
LudlumModel 2218 dual-channelanalyzer to measurethe in situ activityfrom uraniumholdup.A lead
shield/collimatorwas constructed for the detector to provide a 7.5-cm-longcollimatorand 1.5 cm of
shieldingaround the detector that tapered to 0.75 cm around the photomultiplier tube. A 1024-channel
                                                                                      a
multichannelanalyzer (Canberra Series30) was used in parallelwith the single-channel nalyzersin the
                                                        s                            g
Ludlumdual-channelanalyzerto providea pulse-height pectrumof the fission-product amma rays and
art energy calibration to determinethe peaks of interest. The multichannelanalyzer was also used to
qualitativelydetermine the spectrum shifts on a day-to-day basis. A 6-m-longshieldedcoaxial cable
                                          t
carried the signalfrom the photomultiplier ube to the Ludluminstrumentamplifier.The same cable was
used to supplythe highvoltageto the tube.
                                                           a
   A separate 7.5- x 7.5-cm NaI(Tl) crystal/single-channel nalyzer counting systemwas used to assay
cleanoutmaterialsfrom dust generation.This counterwas locatedin a low-backgroundarea of the facility
and used a totally enclosed,lead-shieldedassay chamberto maximizethe signal-to-background    ratio and
hence improve the sensitivityof the measurements.This system gave a signal-to-backgroundratio
improvementof -3 over the in situ measurements,which coupledwith the f~ed detector configuration,
allowedfor greater precisionand accuracy in the measurements.
   All airflowmeasurementswere made in linear feet per minuteof air flowingacross the air inletto the
glove box. These measurementswere made with an Alnor Junior Type 8100 hand-heldvelometerfor
airflowsbelow 800 ft/min (245 m/min). For the higherair velocities,an Alnor Series6000 P velometer,
capable of measuring air velocitiesup to 10000ft/min (3000 m/min), was used. This velometerused a
pitot tube arrangement with a probe, which was inserted perpendicularto the Iaminar airflow. To
accommodatethis velometer,a 75-cm-longrectangularduct extensionwas attached to the air inletfilter,
allowing several measurements across the width and length of the tube. Care was taken that these
measurementswere not obtainedat pointsvery closeto the glovebox faceor the duct sidesas the airflow
patterns along these edges may vary because of “end effects.” With the Alnor Junior velometer,six
readingswere usually recorded at the face of the air inletfilteras a measurementof the airflowinto the
glovebox.


C. Dust GenerationAnd Holdup Measurements

   Uranium dust was generated from three different materials: an incinerator ash containing -1OYO
uranium,a finelypowderedUJ08 with particlesizeup to 45 Urn,and a coarse UjOapowderwithparticle
size up to 200 ~m. Each experimentinvolved 10 dusting cycles wherein 1 kg of the material was
reproduciblypoured from the deliverybottleof the mechanicaldust generatorto the receivingbottle.The

                                                                                                         17
     airflow through the glove box was set at one of three settings(high, medium,or low) by adjusting a
     MITCO control valvelocatedbeyond the exhaustfilterof the experimentalsystem(TableV).
        Sevenseparate experimentswere conductedusingvariousairflowrates and materialscombinationsas
     shownin Table V. Briefly,the dust-generationand holdupmeasurementproceduresincludedthe following
     steps:
        1. The delivery and receiving bottles of the mechanical dust-generatingapparatus were initially
           weighed.A known quantity of U30~(or ash) was placed insidethe deliverybottle and mountedon
           the dust generator.
        2. The airflowcontrol valvewas adjustedto get the desiredflow rate at the inletof the glovebox as
           measuredby a velometer.
        3. Dust generationwas initiatedby openingthe spout of the deliverybottle and starting the vibrator
           attached to the stand (Fig. 7).The dust generatorwas locatedin the glovebox such that the airflow
           through the glovebox flowedacross the fallingU30g(or ash)and carried the dust throughthe glove
           box, ducts, and filters.
        4. The processes of pouring the deliverybottle contents into the receivingbottle and repouringthe
           materialto generatedust were continueduntilz 10kg of the materialwas poured from the delivery
           bottle. The pouring of the contents of the deliverybottle into the receivingbottle constitutedone
           dustingcycle. Each experimenthad 10such cycies.
        5. The deliveryand receivingbottleswerereweighedto determinethe weightlossof materialduringthe
           dustingcycle.
        6. The bulk UJ08 (or ash) in the bottles was removed from the glove box and placed in a shielded
           storage area.
        7. The in sifu holdupof uraniumwas measuredat 14 points(Fig. 6 and Table IV) usingthe shielded
           portable NaI(Tl) crystal and the Ludlum dual-channelanalyzer described in Sec. 111.9.2.These
           measurementswere made after eithereach cycleor a pair of cycles.At the end of the 10thdusting
           cycle, the airflow was reduced to minimizematerial movement in the ventilationsystem, and
           replicatein situ measurementswere made,
        8. At the end of each experiment,the ventilationsystem serving the experimentalglove box was
           carefullydismantledand cleanedout using rags. These rags were carefullycollectedand placedin
           special containers, and the amount of uranium in these cleanout samples was determined
           nondestructively  usinga separate countingsystemdescribedin Sec. 111.B.2.
        Thesestepsof dust generation,in situ holdupmeasurements,and cleanoutmeasurementswererepeated
     for the sevenexperiments.


                            TABLE V. ExperimentalConditions
                                                              Airflow
                                                              Medium      High
                            Materials             (5~fl)a    (45 cfm)” (100 cfm)’
                            Fine UJO~             Expt. 1   Expto2       Expt. 3
                            Ash                   Expt. 4   Expt. 5      Expt. 6
                            Coarse UjOg           ---       ---          Expt. 7
                            ‘1 cfm= 28.32L/rein= 2.832x 10-2m3/min.




18
D. ExperimentalResultsand Discussion

                                                              of
    Sevenexperimentswere conductedduringthis investigation holdupof uraniumin a dust-generating
 operation.The highlightsof the results are presentedin this section.A more detaileddiscussionof the
                                            and                                        the
 modelingof holdupis givenin Sec.111.E, theresultsof NDA measurementsemploying radioactive
 tracer and gamma-rayspectroscopyare providedin TablesC-[ throughC-XV.
    In general,the effectsof varyingoperatingconditionswere reasonablypredictable.For example,the
 change in measuredholdupof uraniumdust on the exhaustair filteras a functionof materialthroughput
 and airflowlevelis illustratedin Fig. 8, As expected,holdupincreaseswith throughputas well as with
 airflow.
    Data collectedat the firstelbow,(measurementlocation8 in Fig.6)provideanotherexampleof material
depositionas a function of throughput as shown in Fig. 9. The dependenceof holdup on operating
conditionsis not as welldefinedas for the falterbecauseof the relativemagnitudeof measurementerrors.
The elbow and filter represent the two extremes of the kind of holdup data obtained during this
experimentalstudy.
    The quality of the holdupestimatesobtainedwas generallyquite good. Weight-lossvalues,which are
simply the differencesbetween the amount of materials at the start of an experimentand the amount
                                                                                        A
remainingat the end of dustingoperations,wereobtainedfor each of the sevenexperiments. comparison
                             v
of gravimetricweight-loss alueswiththeirassociatedmodel-based     estimates(whichusedonlyNDA data)
gives the best measure of the accuracy of the estimate of overall system holdup. Tables VI and VII
summarizethis information.
    For the uraniumdust-generation    experimentsdescribedabove,holdupwas estimatedwithroughly20Y0
accuracy. Had the objectivesof the work been somewhatdifferent,accuracy of -lOO\ocould have been
achieved with the same overall levelof effort. This would have entaileddevotingproportionallymore
resourcestoward measurementof the glovebox floor and filter,whichcombinedrepresent >80V0of the
tolal system holdup but receivedonly about one-thirdof the measurementeffort. Proportionallymore
work on instrumentcalibration also would have improvedthe final holdup estimate.As it was, much
attentionwas givento examinationof materialsdepositionin the 5-m lengthof ductworkthat connected
the glove box and filter even though a relativelysmall amount of holdup was involved.This attention
enabledthe developmentof usefulmodelsfor the variouscomponentsof the system,such as verticaland
horizontal sectionsof ductwork about measurementpoints 6-7 and 11-13.Although differenceswere
observedin the pattern of materialdepositionalong the lengthof the ductwork,no relationshipbetween
holdupand the materials(metaland plastic)used in the constructionof this systemwas identified.
                                                                                  valueslistedin Table
    In practice,it is not possibleto obtain measurementsanalogousto the weight-loss
VI. Data collection usually involves either in situ measurements acquired through use of NDA
instrumentationor measurementsmade followinga shutdown and cleanout of process equipment.The
latter procedure is more time consuming and process disruptive. Of these two alternatives, better
informationis typicallyavailablefollowinga cleanoutsince holdup measurementscan be obtained in a
better environment and, perhaps, using more accurate analytical methods. However, it should be
recognizedthat a cleanoutcannot recover 100%of the actual holdupbecausea smallresidueinvariably
remains. In the contextof this experimentalstudy, the gravimetricmeasurementsof the loss of uranium
from the dust generator is the best estimateof the total holdup withinthe system. Of this amount, the
measuredregionsretain most of the uranium;a smallamounthas escapedthe prefilter.An examinationof
Table VII showsthat the “gravimetric”valuesof the holdupderivedfromthe weightlossof uraniumin the
dust generatorare generallyhigherthan in most other processes.
    When care is exercisedin in situ measurements,however,results can be comparablewith cleanout,
Such was the case in this experimentalstudy (Table VII). Because of the controlled experimental
conditions, use of tracers, and frequent collection of data, estimates of holdup based on in situ
measurementswere as good as those based on cleanout.However,there was no systematicattemptmade
to measure the amounts of uranium that may have passed through the prefilterand escaped from the

                                                                                                         19
                                 I                   I                I       I         I




                           H - Hia AlsfLow Exmnuml
                           M - MU     NSfLOW B@D?lht041
                           L - LOW AIS$LOW tX+ld14ENT
                                                                                            /




                                                  H




                                H




                   o            2                 4               6       8         10
                                                                  (kg)
                                                         THROUGHPUT

     Fig. 8. Change in holdupas a functionof throughputof tineU30, powderat the exhaustair filter
             (measurementlocation 14).


            0.20


                           H - HIGH NS$LOW ~
                           M - MEOIUMAISFLOW ~lM~
                           L - LOW AISFLOW CiFfIflUDO
                                                                          H
            0.15
     a

     3
     0
     x      0.10
     ~
     3
     $
            0.05
                                                                                    L



                                                             ‘L

           0.00
                   o           2                 4                6       8        10
                                                         THROUGHPUT(kg)

         Fig. 9. Changein holdupas a functionof throughputof fine U30s powderat the first elbow
               of the ductwork(measurementlocation8).




20
          TABLE VI. Comparisonof Model-BasedEstimateswith
                    Weight-LossValues’
                                          Airtlow Level
              Material          Low         Medium             High
               Type              (g)            (g)              (g)
             Fine UjO~          3.56           3.11             6.22
                               (4.19)         (3.20)           (6.20)
                                15%             3%               1’%0
             Ash                1.66           1.20             2.50
                               (1.31)         (1.53)           (3.06)
                                27%            22%              18%
             Coarse U~08         ---            ---             1.60
                                 ---            ---            (2.26)
                                 ---            ---             29%
          ‘For each set of experimental             t
                                         conditions,he first valueis the
          estimated                                           The
                    totalsystemholdupobtainedby modeling. second
                                i
          value(inparentheses)s the measured  weightlossof material nd a
                    t
          representshe“best”figure fortheactualamountofmaterialnthe  i
                                                                  b
          system.Thefinalvalueis the relativeerror,or difference etween
          estimate           l
                  andweightossdivided             l
                                        byweight oss.Asisotlenthecase
          withhistoricaldata, the relativeerror here is largerwhensmall
                  of          a           b
          amounts material re involved ecause                     is
                                                 thebackground bigher
                 to
          relative thesource.



                                                     M
TABLE VII. A Comparisonof Holdup Estimatesby DifTerent ethods
                                                     Estimated Holdup (g)
 Experiment
   No.         Material       Aiflow         NDA          Cleanout     Gravimetric
                 Fine
     1           U308          low            3.56           3.59           4.19
                 Fine
     2           U30S          medium         3.11           2,70           3.20
                 Fine
     3           U30S          high           6.22           5.10           6.20
     4           Ash           low            1.66           1.06           1.31
     5           Ash           medium         1.20           1.25           1.53
     6           Ash           high           2.50           2.51           3.06
                 Coarse
     7           U308          high           1.60           1.89           2.26




                                                                                     21
     monitoredregionsof the experimentalglovebox/ventilation    system.It shouldbe reiteratedthat the spiking
     of material in the experiments allowed for considerableimprovementin the qualityof measurementdata
     over what wouldhave beenotherwiseattained.
        The tindings of this investigationconfirm that estimation of uranium holdup in a dust-generating
     operationusingdirectNDA measurementis a nontrivial,time-consuming       task. Cleanoutmeasurementsto
     accomplishthe same objective,althoughhighlydisruptivefor a facilityoperation, may not in all cases
     provideany greater confidencein the holdupestimates.
        It is possibleto obtain high-qualityestimatesof holdupfrom eithermodelingof in situ measurementsor
     from cleanout measurementsif a sufficienteffort is invested.The potentialvalue of holdup estimation
     models should be judged in the context of other options that are availableand the costs and process
     disruptionsthat accompanysuch efforts.


     E. Modeling

       A genericreport2spresenteda nontechnicaldiscussionof the benefitsand limitationsof the statistical
     modelingof materials holdup. Here, modelsfor severalof the componentsare introducedand used to
     developa singlemodelfor estimatingholdupin the entireglovebox/ventilationsystem.

        1. The Filter. The developmentof a holdup estimationmodel for an exhaust air filter,based on the
     physicalfeaturesof the filtersystem,the characteristicsof the airflow,and/or the materialssuspendedin
     the airstream, is extremely difficult.However, careful measurementsof the materials retained on an
     exhaust filter over time and a knowledgeof the materials throughput of the system provide a simple,
     reliablemethodof developinga holdupestimator.Previouswork on the air filterat TA-55 addressedthis
     topic, and a modeldemonstratedin Sec. ILC to havevaluefor holdupestimationon exhaustfiltersis

       h(t) = at + @2,

     wheret denotesthe throughputof the processas measuredfrom the timethe filterwas installedand h(t)is
     the accumulatedholdupat throughputt. The unknownparameters (a,~) dependon operatingconditions
     and are usuallyestimatedfrom the data at hand. Givenestimators(&~)of the parameters,the associated
     functionis

          = tit  ,
       fi(t) + pt’

     which can be used to provide holdup estimates for known throughputs, even for those for which no
     measurementsare made.
       Considerthe data from the low-airflowrun of the UjO~experiment(Fig. 10).The fittedmodelhere is

          = o.0232t+ o.oo14t2,
       Ii(t)

     wherethroughputis measuredin kilogramsand holdupis measuredin grams.Obtainingestimatedvalues
     is straightforward.For example,at the conclusionof the experiment,t = 10kg and the estimatedholdupis
     fi(10)= 0.372 g. A similarapproach can be pursuedfor the resultsof other experiments,thoughthe values
     of (d,~) willbe differentfor differentoperatingconditions(Fig. 8).




22
                    0.5


                    0.4



                    0.3



                    0.2



                     0.1



                    0.0
                           0          2            4           6            8            10          12
                                                               (kg)
                                                       THROUGHPW

                Fig. 10. Holdupof urardumon the filter from the dust-generationexperimentat low airtlow.




   2. Elbows.Considerthe elbowat measurementpoint 8 in Fig. 6. Becauseof the geometryinvolved,the
amount of holdup (per unit area) near the elbowcan be markedly differentfrom that at the top of the
vertical segmentassociatedwith measurementpoint 7. This spatial “discontinuity”means it is usefulto
modelthe elbowseparately.
   The measurementhistoryfor the elbowat location8 for the”low-airflowexperimentwithU~Osis plotted
in Fig, 11. Note the increasein holdup as a functionof throughput.Unlikedata from the falter,however,
there appears to be no strong evidenceof a nonlinearincrease. The holdup model for the area about
location 8 at throughputt is then

  fi5(t)= ,
        65t

wherethe estimatedparameter & is obtainedfrom the observeddata.
  Similarmodelsfor the areas correspondingto measurementpoints9 and 10can alsobe derived;that is,

  fig(t) = &,tand
  6,0(t) = 610t .

In all cases, it is possiblethat if the measurementhistorieswere based on a longertime period,a model
nonlinearin t mightbe appropriate.For the cases at hand, though,linearapproximationsare adequate.




                                                                                                           23
                                           I             I            I            I             I
                                                                                                0

                      0.032


                  9
                                                                                   0
                  &  0.024
                   m                                                                             0

                  L
                  i
                  o
                  = 0.016
                  B
                  3
                  WY
                  !l
                     0.008                 0



                                                        0


                                                                                                 I
                      0.000
                              o            2            4             6            8            10
                                                       Throughput    (kg OF U)

                   Fig. 11. Holdup measurementhistory (for the low-air-flowexperimentwith U30,) at measure-
                            ment location 8.



        3. The GloveBoxFloor. Modelingof the filterand elbowsinvolvedcapturingthe measurementhistory
     by a functionof one variable,h(t), In somecases, a functionof severalvariablesis involved.
        Considerestimatingthe amountof materialthat has accumulatedon theglovebox floorthroughthe use
     of measurementsobtainedfrom detectorssuspendedat a heighth over the floor. Figure 12 depictsthis
     situationwhenthree measurementlocationsare employed.At throughputt, letthe functiond(t,x,y)denote
     the densityof materialat location(x,Y)on the floor.The total holdupis then

       h(t) =f ~ d(t,x,y)dy dx ,
             00

     where(L,W)denotesthe (length,width)of the glovebox floor.The objectiveof modelingis to usethe data
     to developan estimateddensityfunctiona(t,x,y)and estimatethe holdupby

        Ii(t) ~ a(t,x,y) dy dx
           =j                      .                                                                          (4)
             00

                                                                 run
        The data usedfor this applicationarisefromthe low-airflow of the UjOaexperiment.The glovebox
     floor is 132x 66 cm, and measurementsare collectedfrom a heightof 97 cm abovethe three locations:

       (x,y)= (13.97,42.55),(54.61,31.75),and (97.79,34.29).

                                                                          a
     The measured amount of material accumulatedon the wallswas negligible, nd the depositionon the
     ceilingof the glovebox was assumedto be negligible.




24
                                                                      D3
                                                                      A
                                             D1
                                             A
                                                         D2
                                                                             h
                                                         4

                                                                         /
                                                                      4
                                                                      .. .
                                                                   ,.
                              /                                    (X3,Y3)                   /
                                             T
                                         (x,:Y,)         ;
                          /                                                         /
                                                         i
                                                      (x,:Y,)
                                                                                        -x
                                                    suspendedvera glovebox floor.
                              Fig. 12. Threedetectors       o



  To developthe model,it is usefulto considera singlemeasuredvalueobtainedover location(X1,Y1)   at
throughputt (see Fig. 13).The limitingvalueof the holdupat the point(x,y)recordedby the detectoris


               (          d(t,x,y)
                                                      (y
     n(t,x,y)= % h2 +(X - X1)2+(y - y1)2 if (x - X1)2+ – yl)2 < rz ,
                [0                                 otherwise

                      +
where h2 + (x – X1)2 (y – yl)2is the square of the distance betweenthe detector location and (x,Y),r
reflectsthe “range of vision”of the detector,and the normalizationconstantc1correctsfor such factorsas
eiliciency of the measuringdevice. For the example,r = 34.3 cm. The detector above (x1,Y1),      which
receivessignalsfrom many locations,records an integralholduprepresentedby
                 66132
     N(t,xl,yl) = ~ ~ n(t,x,y)dx dy      .                                                           (5)
                     00


In practice, the limitingvalue of holdup n(t,xl,yl) cannot be measured directly,and this adds a minor
complicationto derivationof the estimatedfunctiona(t,x,y).However,the processof integrationin Eq. (5)
“smooths”n(t,x,y)about a regionof (xl,yl).If the densityfunctiond(t,x,y) is approximately linear in x and
y or if the range of visionof the detectoris sufficientlysmallto ensurethat d(t,x,y)doesnot changemuch
for (x,y) in that range of vision,then net count rates can be calibratedas if the materialwere uniformly
spread over that range.
   A first step in modelingis to determine,to whateverextent possible,the form of the densityfunction
                                                     I
d(t,x,y).The modelused for the GA Technologies, nc., data is

     d(t,x,y)= at + ~tx + fiy ,                                                                      (6)

where t denotesthroughput and (a, (3,y) are unknown parameters.The postulatedmodelfollowsfrom
                                         a
standard response-surfacemethodologyzs nd is easilyinterpreted.At a givenlocation(x,y)on the floor,
the densityincreasesproportionallyto throughput.At a giventhroughputt, the densityvarieslinearlyas a
functionof x and y. Uniformdepositionis includedas a specialcase (~ = y = O).Of course,other formsof
densityfunctionsbesidesEq. (6) could be consideredif warranted by the data.



                                                                                                            25
                                                    D,
                                                   A




                                             Fig. 13. A singledetector over (x,,Y,).




       Substitutionof Eq. (6) into Eq. (5) yieldsthe relationship

       N(t,xl,yl)=at    c1       JJ                           [h’ +(X - X1)2+ (y - y,)’]-’ dx dy
                       { (x-x1)2 +(Y-Y1~ <r’                                                    1
                                  0   <X    < 132
                                  o<       y< 66
                 +pt    c,        JJ                          x[h’+(x -xl)z+(y–yl)z]    ‘ldxdy
                       { (x -xl)’ +(y-Y1)’<              r’                                      }
                                  O<x<        132
                                  O<y<        66
                 +yt    c1        (J                          y[h2+(x -x,)’ +(y-y1)2]-’dx     dy
                         (x -xl~+(y-yl)’<r2
                                  ()<x < 132
                                  0 <y <66


     Though nontrivialto compute,the integralsin bracketsare constantsand N(t,xl,y,)is a linearfunctionof
     the unknownparameters (a,~,y), Similarly,integralholdupvaluesN(t,x2,y2) nd N(t,xl,yq)are also linear
                                                                            a
     in the parameters.
        These observedholdupvaluesare “true” holdupmeasuredwith error, and from them can be obtained
     estimatedparametersin the linearmodel.The estimateddensityis then

              =
       a(t,x,y) tit ~ ptx +jiy,                                                                          (7)

     which is integrated as in Eq. (4) to providethe holdup estimator fi(t). For this model, h(t) is a linear
                   f s
     functionof (&,3,~) o that error propagationis straightforward.
                                                                    run
       As an application,considerdata collectedfrom the low-airflow of the UJO, experiment(Fig. 14).
     Note the approximatelylinearincreaseof the net counts withrespectto throughputexhibitedat allthree
     locations.Also,the observedholdupappears relativelyuniformacrosslocations,in thisinstancereflecting
     the smoothingdiscussedpreviously.


26
                                        [           I                          I                           I                                E
                                                                                                                                          ....
                                                                                                                                    ,..
                                                                                                                              ...
                                                                                                                        ,.,
                       +        —    +ILOCATION3                                                          0      ..””
                       e........elJXATKIt4    4                                                                  ”
                                                                                                               ,.”
                       &         ALOCATION5                                                            ,.,..”’
                                                                                                 ...
                                                                                           ...
                                                                                       ,.,”
                                                                                    ...
                                                                              ...
                                                                          ..,”
                                                                       ,..
                                                                 ,..
                                                              ,..
                                                        ..”




                                       2            4                         6                           8                                 10
                                                        THROUGHPUT(kg)
                                                         o
                                     Fig. 14. Measurements n thegloveboxfloor.



                                                                                    rejected,indicating
  Upon fittingthe modelto the data, a joint hypothesisof (~,y)= (0,0)is significantly
nonuniformdeposition.The estimateddensityis higherin the regionabout (Xl,yl)= (13.97,42.55)than in
                     =
the regionabout (X3,YJ)(97.79,34.29),confirmingsuspicionsbasedon visualinspectionofthe glovebox.
The estimatedholdupat the end of the experiment,t = 10 kg, is
           66132
   fi(lO)= ~ ~ il(lO,x,y)dx dy
           00
         = 2.68g ,

which is in good agreementwith the cleanoutvalue,2.71 g.
   Use of the predictiveEq. (7) is relativelystraightforwardand parallelsusageof the modeldevelopedfor
the filter.Model-basedestimatescan be used for estimationof holdupfor a briefperiodinto the future,at
which point additionalmeasurementsare requiredto validatethe modeland update parameterestimates.
For thesepurposes,futuredata neednot be collectedat the same locationsnor withthe samefrequencyas
in the initialexperiment.

   4. The Verticaland HorizontalDucts. Risingfrom the top of the glovebox is a verticalpipe(segments
6 and 7 in Fig. 6). To developthe modelfor thiscomponent,it is necessaryto introducesomenotationand
the mathematicalconceptsused here,
   Whenmeasuringholdupthat has accumulatedon the interiorsurfaceof a verticalcylinder(or pipe),the
experimentermust deal withthe geometricalaspectsof the problem.Becausethe “range of vision”of the
detector is a cone emanating from the point of measurementand holdup is depositedon a cylindrical
surface,modelingis most easilydevelopedusingsphericalcoordinates.




                                                                                                                                                 27
       Consider a set of points in three-dimensionalspace. In the “usual” coordinate system, a point is
     describedas (x,Y,z)as in Fig. 15.

                                         z

                                         I   . . . .   ...
                                                              (X.Y,ZJ




                               (0,0,0)                                                                -Y




                          x                                  Ixi.   yloal -
                                                                        1     DIIcc-   *       -    @, CO~ ~   qin   . . ~~n*I   8


                                                         “*” % -
                                                         {0.0,01 to
                                                                          Fi-Tz
                                                                          (E1?Y1,llI       .
                                                                                                   ‘s ‘h” ‘l”’””” ‘r”’


                                                                                         s
                                         Fig. 15. Sphericalcoordinatesin three-dimensional pace.




                                                                            we
       If we were lookingfrom the point (0,0,0)toward the point (XI,YI,O), wouldhave to raise (or lower)
     our sights to see the point (Xl,yl,Zl).Letting 1$denote the angle through which we raised our sights)it
     followsthat



     where




                                                                         we
        If we were lookingfrom the point(0,0,0)toward the point(xI,O,O), wouldhave to turn our headsto
     the left(or right)to seethe point(xl,yl,O).Letting+ denotethe anglethroughwhichwe turnedour heads,
     it followsthat

                 ~   $
        Xl= DI COS COS

     and

        y, = D, cos ~ sin 1$

                                               i
     becausethe distancefrom (0,0,0)to (Xl,yl,O)s

        {~+      y: “ = D, COS$ .

     The three-dimensionalcoordinate system is thus “transformed” from one involving(x,y,z) into one
              the
     invcslving distanceI) = X2+ y2+ Z2and the angles(~,e).


28
  Now considermaterialheldupon the interiorsurfaceof a verticalcyclinderthat is beingmeasuredby J
                                                           =         and
detectors.Let the detectorsbe locatedat the points {(x,y,z) (O,O,ZJ)}, letthe centerof the cylinderrun
                                            In
verticallythroughthe point(x,y,z)= (c,O,O). other words,the detectorsare stackedverticallyabovethe
point (0,0,0),and the center of the cylinderruns parallelto the lineof detectorsand is a distancec away
(Fig. 16).



                                      I




              LOCATION   2
              (X,Y,Z) = (0.0,106.7)
                                      ,

                                                                            +
                                                                            ‘i==
                                                                             r




                                                                            =--l-’
              LOCATION   1
              (X,Y,Z) = (0,0,0)




                                          I
                                          I




                                      z



                                      L-                x
                                                                      INTERIOR

                                                                            OF
                                                                              RADIUSOF PIPE= r

                                                                      CENTER PIPERUNSVERTICALLY

                                                                      THROUGHTHE POINT(X,Y,Z) = (C,O,O)

                                                                      PIPERUNS213 CM (Z= -61 TO 152)

                                          Fig. 16. Sideviewof detector and verticalcylinder.




                                                                                                          29
        If the verticalcoordinatez takes on valuesfrom a to b and r is the interiorradiusof the cylinder,the set
     of pointson the interiorsurfaceis

                     I
          S = {(x,Y,z) (x - c)*+ y2= rz and a < z < b}.

                                                                        +
     Expressedin the sphericalcoordinatesof Fig. 16,the equation(x – C)2 y2= rz is equivalentto

          (D cos ~ cos 0- c)’ + (D cos $ sin 0)2= r’ ,

     or

          [COS2 + [-2c cos 1$ (3]D+ [c*- r’] = O.
              I$]D2         cos                                                                             (8)

     Note that for f~ed line of sight ($0), this is a quadratic function in the distance D. The two roots
                                                                           the
     correspondto the pointswherethe lineof sight“enters”and “leaves’’ cylinder.Callthe roots D~ln(~,o),
     and D~,X(~,O)(Fig.  17).
                                  =
        From its location(x,Y,z) (O,O,zj),  thejth detectorcan seeup/downfrom angle–A to +A”. The same is
     true from right to left, althoughit is clear from Fig. 17 that the cylinderliesentirelywithinthe right/left
     angleOfor

          9 &(sin “[-r/c], sin-’ [r/c]).

        Thejth detectorreceivesnonzeronet signalsfrom alllocationsin the intersectionS fl R,, whereS is the
     interiorsurfaceof the cylinderas beforeand RJis the rangeof visionof thejth detector.For thedetectorat
     location 6, (x,y,z)= (0,0,0),wehave

          R = {(D,~,11) D >0, sinz~ + sinzOs sinzA} .
                      \

     The postulateddensityfunctiontakes the form

          d(t,x,y,z)= at + fltz.




                              NOIZ : M   ANUI wMTW   HORQONWL $. OOESNOTAPFIAR IN All OYVtHEAOW



                                           Fig. 17. Overheadviewof detector and verticalcylinder.




30
This is interpreted as follows:
  1. At a given location (x,y,z), the amount of material increases proportionally to throughput t.
  2. At a giventhroughputt, the densityvarieslinearlywith heightz but does not dependon x or y. The
      differencein air velocityat the top and bottom of the pipeservicingthe glovebox accountsfor the
      change in materialdepositionas a functionof height.
Expressedin sphericalcoordinates,the densityis

  d(t,D,$,O) at + ~tD sin r$,
           =                                                                                                       (9)

                                                    =
   Considerthe measurementfrom location6, (D,i$,O) (0,0,0).For a givenlineof sight(~,9)in the range
                                                                                                and
of visionRbof the detector,nonzeronet signalsare receivedfromtwo locationsat distancesD~ifl(I#,8)
          as
Dro8X(@) indicatedin Fig. 17.The integratedvalueof the holdupat this locationis the collectionof all
such signalsin Rb; that is, analogousto Eq. (5) from the modelingof the glovebox floor, the value of
N(t,O,O,O)from location6 satisfies




  The roots of the quadratic Eq. (8) are

   Drnj.(0,6)=     c--&(Cos e -           / (r’/c’) - sin’ 8 ]                                                    (lo)

an,d

   Dm. ($,0= C*                 ICose + / (r’/c’) - sin’ 6 ] .


                                               and        as
Substitutingd(t,D,@3)as in Eq. (9) and D~in($,13) D~,X(~,O) in Eq. (10)gives
                                 sin-l(r/c)     sin-’ ({sin’ A - sin’ 0)
            =
   N(t,O,O,O) at           c1         f                s
                       (         sin-l(–r/c)    sin-l(–    sin’ A - sin2f3)




                   (
                                      COS2~
                           c’ [cos 0 – (r’/c’) – sin’ o]’ +       6
                                                                      COS2 $
                                                                                 —
                                                            c’ ICOS + @/c’) + sin’ 0]2
                                                                                                 1)  d+ df3




                            (
                                  sin-’(r/c)    sin-l (ysin’ A - sin’ 0)
                   + pt c,
                                      J               J
                            \     sin-*(–r/c)   sin-*(–    sin2A – sin’ 0)

                                  sin $ cos $                           sin $ cos $
                           c [cos6- ~(r2/c2) - sin’ 9] +         c [cos o -~)         - sin’ fj] ‘$ ‘“        “
               {                                                                                1)




                                                                                                                         31
     “I_heintegrals in brackets are constants  for fixedvaluesof r, c, and A. Once these integrals are found,
     estimation of the parameters (a, ~) can be pursued os with the example of the glove box floor.
     Corresponding integrals exist for the integratedholdupat other locations.Thisyieldsan estimateddensity
     functionand thus estimatedholdup.
                                   I
        For the GA Technologies, nc., data, we haver = 5 cm, c = 40.7 cm., and A = 19.2°.The detectorwas
     placed at locations6 and 7, (x,y,z)= (0,0,0)and (0,0,106.7cm), respectively.Data from the low-airflow
     run of the UJOa experimentare plotted in Fig. 18, and the estimated density function is. in units of
     milligrams per square centimeter.


       a(t.D,@3)= 0.00198t+ 0.0000273tD sin +.


                                         {              I                 I             I         I

                                  A        6
                                    LOCATION                                                     0
                                           7
                                  u LOCATION



                                                                                                 ./’
                                                                                              ,/ ~
                                                                                        ‘,/
                                                                                   ,/
                                                                              ,/                 0


                                                                     ,/

                                                                ,/

                                                        ?/

                                                   ,/

                u                        c1   ./

                                                                          A




                                                                          1             I         I
                     0.00
                            o            2              4                 6             8        10
                                                             THROUGHPUT(kg)

                                          Fig. 18. Measurements on the vertical cylinder.




     As expected,the estimateddensityincreasesas a functionof the heightD sin ~. At the conclusionof the
     experiment,t = 10 kg and the estimatedholdupis

        fi(lO)= ~a(10,D,!,9) dD d$ dO
                s
              = 0.168 g .

     This valueagreesreasonablywellwith the NDA measurements.
       The horizontalsegmentof ductwork,roughly2 m longand coveringmeasurementpoints 11-13,can be
     modeledusingthe sameprinciples.A firststep in suchmodelingis to lookfor change(or lack of change)in
     holdupover the segmentof ductwork.In contrast to data fromthe verticalsegment,materialsdeposition
     here did not appear to differfrom locationto location,and thus a simplermodelcan be used.A plot of the
     measurementhistoriesat locations11-13from the low-airflow     experimentwithUJO~is givenin Fig. 19.



32
                                    I           I           I           1           I
                             s   LOCATION
                                        11                                         A
                             q          12
                                 LOCATION
                             A   LOCATION13                                        s
                                                                                   q
                                                                                   q




                                                                       A           6

                                                                       s           s



                                                           q




                                    a




                                               s
                                    m
                                               A


                                    L          1            I           I           I

                         o          2          4           6           8           10          12
                                                             (kg)
                                                    THROUGHPUT

            Fig. 19. Holdup measurement history (for low-airflowmeasurementswith UjO*) at locations
                      11-13.

    If materials depositionwere uniformthroughoutthe length of the duct segment,data at each of the
measurementpoints could be used to estimate the total amount of holdup. As at the elbows,a linear
increase in materialsdepositionas a function of throughput is indicatedby the data. A model for the
densityof material(holdupper unit area) at locations(x,y,z),wherethe leftend of the horizontalsegment
is taken for convenienceto be at (0,0,0),is

  d~(t,x,y,z)= ah t.

That is,the densitydependson throughputt but doesnot dependon the location.The estimatedholdupfor
the segmentof ductworkis then

   fi(t) dh(t,x,y,z)dx dy dz
      = f
          s
        — Aii#
        -         ,

whereS again denotesthe duct’sinteriorsurface,A is the associatedsurfacearea, and &hisestimatedfrom
the data.

   5. Modelingthe GloveBox System.Once modelsfor the componentsof the glovebox system(such as
filter,glovebox floor,or horizontalduct segment)have been developed,they can be combinedto yielda
modelfor the systemas a whole.The estimatedsystemholdupis simplythe sum of the estimatedamounts
of holdupin each of the components.A modelfor the systemcan be obtainedby “adding”the modelsfor
the individualcomponents.An exampleof this for the low-airflowexperimentwith UJOgisgivenin Table
VIII.
   It is importantto note that the estimatedparametersfor a givencomponentmay be difficultto obtain,
as in the casesof the glovebox floorand verticalsegmentwherenonuniformdepositionmustbe accounted
for and integrationof an estimateddensityfunctionis involved.Also, when updatingthe modelfor the

                                                                                                        33
     TABLE VIII. Summaryof ModelingResultsfor Low-AirflowExperimentwith U~O~b
                               Measurement      Modelfor Low-Airflow        Estimated Holdup(g)
     Component                   Point’         Experimentwith UJOBb        Throughput= 10 kgb
     Glovebox sides                 1-2           h,(t) = o                          0
     Glovebox floor                 3-5           fi~t)= 0.2677t                   2.677
     Verticalsegment                6-7           fi,(t)= 0.0168t                  0.168
     First elbow                     8            fi,(t)= o.oo27t                  0.027
     Segmentbetween                  9            fib(t)= 0.0086t                  0.086
      elbows
     Secondelbow                    10            Ii,(t) = 0.0036t                 0.036
     Horizontalsegment             11-13          fih(t)= o.o195t                  0.195
     Filter                         14            fi~t)= o.0232t                   0.372
                                                        +o.oo14t2
     Systemtotal                    1-14          fi(t)= o.3421t                   3.561
                                                       + o.oo14t2
     Systemweightloss                                                              4.193
     ‘See Fig.6 fordetails,
     %e number                figures
                  ofsignificant                  dataincolumns and4 ofthistableisnota representation
                                    inthetabulated             3                                   ofthe    “
              of          e
     accuracy modeling stimates.                       errorsofestimations.
                                   SeeTableVIforrelative



     system (that is, using additionaldata to check modelperformanceand update parameter estimates),the
     individualcomponentsmustbe updatedseparatelyand re-addedto givethe revisedsystemmodel.Perhaps
     the primary valuein developingan overallmodelfor the systemis to characterizethe systemholdupas a
     functionof relevantvariablesfor a givenset of operatingconditions.For example,resultsfrom the low-
     airflowexperimentwith UjO~indicatedthat, beginningfrom a “clean” state, holdupinitiallyaccumulates
     roughly proportionallyto throughput. Of course, the same need not occur under other operating
     conditions.

        6. Comparisonof Experiments.The modelsused in allexperimentalwork are of the same structure as
                                                      run
     those describedin great detailfor the low-airflow with UJO~.Thus, it is not necessaryto repeat that
     modeldevelopmenthere.The only (minor)differencesin modelingoccurred when the cleanoutfrom the
     previousexperimentlefta smallamountof materialfor the beginningof the nextone.A term was addedto
     the modelto accountfor this when necessary.
        The effects on holdup of varying operating conditionswere reasonably predictable.Increasing the
     airflow level deposited additionalmaterial into the ductwork and filter. Not only was the amount of
     materialin theselocationsincreasedbut so was the fractionof the total systemholdupresidingthere. Use
     of tine UJ08 powdergeneratedthe mostholdupof the threematerials,withash next,and finallythe coarse
     U308material.
        Throughout the experiments,holdup behavior at the individualmeasurement locations remained
     relativelystable. On the face of the glovebox (measurementlocations 1 and 2 in Fig. 6), there was no
     indicationof appreciablematerialdepositionas a majorityof the net count rates obtainedwere negative.
     Holdup on the glove box floor (locations 3-5) exhibited nonuniform deposition with the greatest
     concentrationof material usually on the portion of the floor beneath the verticalsegmentof ductwork
     rising from the glovebox. On the interior wallsof the verticalsegment(locations6 and 7), deposition

34
increased as a function of height. At the two elbows and adjoiningsegment(locations8-10), holdup
accumulatedin an approximatelylinearfashionwith respectto throughputat each measurementpointas
                        The
describedin Sec. 111.E.2. horizontalsegmentof ductwork (locations11-13)exhibitedno evidenceof
ncmuniform  deposition;that is, in contrast to the verticalsegment,there was no significantdifferencein
accumulatedholdupamongthe three locations.Finally,measurementson the filter(location14)exhibited
a nonlinearincreasein holdupin accordancewith the modeldiscussedin Sec. IILE.1.


I~To   EXPERIMENTAL     STUDY    OF   URANIUM     HOLDUP     IN   A LIQUID-LIQUID     EXTRACTION

       PULSE COLUMN

   Liquid-liquid extractionprocessesfor the separationof uraniumand plutoniumfrom fissionproducts
and other impuritiesare widelyused in nuclearfuel-reprocessing  plantsand scrap recoveryoperationsat
nuclear fuel materials preparation and fabricationfacilities.The chemicalseparation processesfor the
extractionof uranium and/or plutoniumare based on the differencesin the abilitiesof the nitrate salts of
cations to form neutralcomplexeswithtributylphosphate(TBP).These neutralcomplexesare lipophillic
and are solublein an immiscible                                                A
                                 TBP phase,wherethey are essentiallyun-ionized. ctinideelementsin the
+4 and +6 valencesform strongercomplexesthan almostany other element.Metalnitrate salts in which
the metal valence is +1, +2, or +3 are virtually not extractableunder these conditions.These features
providethe basisfor PUREX separationfor spentfuelreprocessingand extractionof SNM duringscrap
recoveryoperations.
   In practice. the separation and purificationof uranium and plutoniumare achievedusing a seriesof
sclvent-extractioncontractorsin which uranium and plutoniumare selectivelyextractedinto the organic
phase containingTBP through countercurrentaqueousand organicstreams.Three commonliquid-liquid
                       are              p
extractioncontractors mixer-settlers, ulsecolumns,and centrifugalcontractors,
   The objectiveof this investigationwas to attempt to developholdup estimators for a pulse-column
liquid-liquidextraction system using concentration profiles developed from extensivesampling and
analyses during steady-stateoperations of the pulse columns. The principlesused in developingsuch
estimates of SNM inventoriesare applicableto estimatingmaterials holdup in liquid-liquid    extraction
cemtactors during steady-state operations as well as in valved-offand drained column conditions.
Significantquantitiesof SNM remain in these pulse columns during steady-stateoperationsand plant
shutdownconditions.The runout inventories(residualholdup)of the pulsecolumnsafter a solutiondump
are smallcompared with the in-processinventories.All these inventoriesare of importanceto materials
accountability;however,estimatingthe columninventoriesin an operatingplantis extremelydifficult. heT
method of estimatinginventoriesof SNM in liquid-liquid    extraction systems by means of direct NDA
techniques is desirable,although such measurementshave yet to be fully developedfor a processing
fa:ility.
   In a recent attempt to determinethe residualholdup of uranium in pulsedextractioncolumns,three
pulsecolumnsat the Y-12plantin Oak Ridgewereflushedout with50V0        HNOJ, and the uraniumcontents
of the cleanout solutionswere determinedusing a solution-assaysystem.The resultsof these measure-
ments’ indicatethat only - IV. of the steady-stateinventoryof the column remained as residual holdup
after column dumps. The average valueof the inventoriesof HEU in the three columnsbeforedumping
was 6 kg of HEU, and the averageresidualholdupof uraniumin these columnswas <80 g. Attemptsto
perform in sifu measurementsof this residualamountof uraniumin an operatingplantwiththe associated
spatial distributionof uranium in the column and radiation background problems caused by uranium
inventoriesin the vicinitywouldonly have been a futileexercise.
   The experimentalstudiesdescribedhere offer an alternativeapproach of developingholdupestimation
modelsfor the pulsecolumnfrom knownprocessparametersand a limitednumberof measurements.




                                                                                                           35
     A. ExperimentalStudy

        A pilot-scalepulse-columnprofilestudy was sponsoredby the Los AlamosNationalLaboratory at the
     AlliedGeneral NuclearServices(AGNS) facilitiesat Barnwell,SouthCarolina.zs                      s
                                                                                    This experimental tudy
     was designedto investigatepulse-columnoperationsusingonly uranium,The pulsecolumnsof this pilot
     facility were equipped with samplers along the length of the column to collect samples for uranium
     analyses and to develop the profile of uranium within the column during steady-stateoperations, In
     addition, a few analyses of the column dumps were performed to assess the value of the integrated
     inventoriesdevelopedfromcolumnprofiles.Althoughtheprimarypurposeof thesepilot-scale       experiments
     was to assess computer programs developedfor pulse-columnprotiles,the data obtained during these
     experimentalstudiesare valuablefor developing holdupestimatorsor columninventoriesof uraniumafter
                                                      sections,detailsof the pilot-scale
     steady-stateoperationsare reached.In the following                                            s
                                                                                       experimental tudies
     are presentedwith emphasison two experiments(2A-3 and 2D-2)relevantto this holdupstudy.The data
     from these experimentsare used in the developmentof estimators for uranium holdup in the pulse
     columns.


     B. Equipmentand Facilities

        The equipmentused for the two experimentsconsistedof two glass pulse columns(1A and IB) as
     illustratedin Fig. 20. Auxiliaryequipmentincludedcirculationpumps as wellas stainlesssteeltanks for
     feed solutions,product(s),and waste(s).Column 1A, with a diameterof 5 cm, was an extraction/scrub
     pulsecolumnwith a heightof-8 m. Column IB was a strippingcolumnwith a diameterof 7.5 cm and a
     heightof -6 m. Bothpulsecolumnshad 0.15-cm-thickplatesspaced 5 cm apart with -23V0 free surface
     area and plate orificediametersof 0.3 cm each. Both pulse columnshad top and bottom disengaging
     sectionsmade of glass.The top sectionwas ventedand the bottom one was connectedto a bellows-type
     pulser.The aqueousand organicinterfaceswerecontrolledautomaticallyat the bottomof the disengaging
     section of column 1A and at the top section of column IB using two titaniumconductivityprobes to
     regulateair-operatedcontrol valvesat the aqueous-phaseoutlet.
        The pulsecolumnswereprovidedwith samplingports as shownin Fig. 20 (Al-Al 1 and B1-B7).There
     were fivesamplingports alongthe scrubbingsectionof column 1A and six alongthe extractionsection.
     The strippingcolumn IB had a total of sevensamplingports.


     C. ExperimentalProcedures

       Unirradiateduranium was used as the solutein these pilot-plantexperiments.The experimentswere
     designedto obtain detailedaqueous and organic concentrationprofilesand fractionalphase volumesas
                                                                      s
     wellas the uraniuminventoryof the entirecolumn.The experimental etupincorporatedboth of the pulse
     columnsdescribedearlier.The center-fedextraction/scrubcolumn had an aqueousfeed (IAF) with the
     TBP extractantin an organicsolvententeringat the baseof the column.The organicproductfromthe first
     column was allowedto enter the second column as a bottom-fedstream, and uraniumfrom the organic
     phase was stripped into an aqueous stream entering at the top of the second column. The operating
     conditionsof the columnsduringtheseexperimentalruns are summarizedin Table IX.
       During experimentalruns, steadilyoperatingpositivedisplacementpumpswere used for feedingeach
     pulse column with correspondingfeed solutions. When the pulse columns were at steady state, as
     determinedby uranium assays at the end of the streams, samplesof aqueousand organic phases were
     collectedfor analysis.The results of these analyseswere used to developthe concentrationprofilesof
     uraniumin the columns.Uraniumconcentrationsweredeterminedby densimetricor titrimetricmethods.



36
        I As       ,




            F
                           IAP
                                 —                            IBX
                                                                           .
                                                            15cm                IBW
                                                              +
        A-1

        A-2                                                  ~
                                                             B-1
        A-3                                            7.6 cm>

        A-4                                                      B-2
               f
  IAF A-5
      A-
                                                               B-3
    +                                                                              E
        A-7                                                                       o
                                                                                  a
                                     h-
        A-8                          AI                          B-4
               !
        A-9- –
                                                                 B-5

     A-lO- –
    5 ;m                                                         B-6
        ~          —


       A–1I
   I AX




                   L         IAW

      COLUMN 1A
(Extraction/SCRUB)                                            (STRIPPING)
                   Fig. 20. A schematicrepresentationof the pulsecolumnsused.




                                                                                       37
                 TABLE IX. Pulse-ColumnOperatingConditions
                                               Column 1A                 Column IB
                   Process Parameters        (Extraction/scrub)          (Stripping)
                   Run no.                     2A-3 & 2D-2              2A-3 & 2D-2
                   Feed inlet                  650 mL/min                     ---
                   Strippingsolutioninlet            ---                1130 mL/min
                   Pulsefrequency                 82/rein                  60/min
                   Pulse amplitude                 2 cm                     2 cm
                   TBP concentration               30Y0                     30’%0
                   Originalsolvent              n-dodecane               n-dodecane
                   HNOj Concentration              2M                     z 0.01 M



     The inventoriesof uranium in the columns were also determinedby analyzingthe column dumps by
     measuring both the volumes and concentrationsof uranium in the partitioned phases of the dump
     solutions.


     D. UraniumConcentrationProfilesof PulseColumns

       Typical uraniumconcentrationprofilesof the two columnsused in these experimentsare as shownin
     Figs. 21 and 22. Figure 21 showsthe concentrationprofileof the extraction/scrubpulsecolumn(1A) in
     whichthe aqueousphasewas dispersed.The aqueousuraniumconcentrationsobtainedduringanalysesof
     samplesthat had reached equilibriumdid not necessarilyreflectthe actual concentrationsof uraniumin
     the columnat the timeof sampling.Therefore,a methodproposedby Gier and Hougen29     wasemployedto
     determinethe actual concentrationsof uranium at the time of sample withdrawalfrom each sampling
     point along the column. Concentration profiles thus developedfor experiments2A-3 and 2D-2 are
     presentedin Tables C-XVI and C-XVII, respectively.


     E, Pulse-ColumnInventoryEstimation

        The most straightforwardmethod of estimatingthe amount of material in a pulse column entails a
     cessationof columnoperationfollowedby a cleanoutof material.Though usefulin providinginformation
     for accountabilitypurposes, such an approach is very disruptiveand thus could be performed only
     infrequently.The developmentof estimates not requiringprocess disruptionswould be of substantial
     benefitto facilityoperationas wellas to materialsaccountability.
        The quantityof materialto be estimatedhereis the sumof the amountsof uraniumin differentportions
     of the column.Considera hypotheticalsituationas depictedin Fig. 23. The column’sworkingsectionhas
     20 stages, and the amount of uraniumin each stage is plotted as a functionof stage number.The total
     amount of uranium is the sum of the 20 values,which is equal to the shaded area under the column’s
     concentrationprofile.
        Given measurementsfrom differentstagesin the column,acquiredeitherby NDA measurementsor by
     chemicalanalyses,it is possibleto estimatethe profile.Mathematicalintegrationof this profileyieldsthe
     estimateof uraniumin the column.The two primary sourcesof error in this estimateare
        q uncertaintiesin the measuredvaluesof uraniumfor the sampledstagesand

        q uncertaintyresultingfrom interpolationover any unsampledstagesin estimationof the profile.




38
                                                               #




                .




               ....




               ....
               ....

               ....
ORG



                                   ‘C(A),

               I
                (A)
                      URANIUM               CONCENTRATION                      (g/l)
      Fig. 21. Uranium concentration profile of the extraction/scrub column.
%          w
                                      –C(o)l




                                                       ‘C(A)




                                                       \
                                                       \
                                                           \
                                             I                 \
                                                                   y(o)
                                                                       \
                                                                           \
                                                                               \
                                                   I                               \
                                                   I
                                                                                       \
                                                   I
                                                                                           o


        It
    +

                                                                           C(A)4
        ‘-HA)                                                      #
                                                                                               )
        Fig. 22. Uranium concentration profile of the stripping column.




                                                                                           a

                                                                                                   a
                                      STAGENUMIXR                                      OOTl&lMf

        Fig. 23. A hypothetical concentration profile of uranium concentrations.




    a

                                          a



                                                                                                  a
                                                                     a

A




                                                                                   a
                                              a



A                                a
                                                                                  a




                                                                                                          a

                                                 a
         a                                                                             a
                                 a


     a                                                                                                a                  a



             8



                                                                                               -
                                                                                           *-cmAtec
                                                                                           u
                                                                                                          PHAsE
                                                                                                          PNAsE
                                             T
                            /
                                .7”           k
                                               \
                       )(                            \,
                 ,,/                                      T
                                                          \
                                                          \
                                                              \
                                                                  \
                                                                      \
                                                                          \
                                                                              \


                                                                                  \
             2                                                                    \
                                                                                   i
                                               q.
                                                ,
                                               ,.                                   \

                   1                               =AGf NUMBER
                                                                                                               BOTTOM
                 &wN                                                                                          OFCOLUMN

                            Fig. 24. Estimated profile-piecewise                      linear approximation.




42
                                                           x
             {                                                                 a




                    ,.,......
                                                         z-
                 ,’~            k                                  P
                                                         D - AQUEOUSHASE




A




2

                                u




                                                          .
                                                          .

0
      1                             STAGENUMBER
    TOPOF                                                               BOTTOM
    COLUMN                                                             OF COLUMN

                 Fig. 25. Estimated profile-regression    methods.
        +               -                         ,



=                   +       -                 +           .




    a                                                 a
                                          {


                                                              x =O
                    x=



                .
0


            g                                 a

                                                                a
        d




                            YZ, ..., y$
                    =            a



                                     a
                    a




    =
    =




            a




                                             A

                             a



A
                a       L.

                                     a
                                 a




                                 a
                                         a




        g
                                                                                       x–
                                               -mx.... -                               u        P
                                                                                        - AQUEOUS NASE
                                       -----
                                      ”
                              ,., .,. x
                        ,.,                                    :?,
                  .,,                                                ‘.
            ,.,                                                        ‘.
         ,,”                                                            ‘$
                    x
                                                                          ‘.x




                                                           o
                                    o


     o
             1                                                            NUMBER
                                                                      STAGE
         TOPOF                                                                                                BOTTOM
         COLUMN                                                                                              OF COLUMN

                                        Fig. 26. Estimated profiIe-Burkhart            model.



          TABLE X.                    Summary of ModelingRemdts
                                                           ExoedmesstalRun 2A-3
                                                                Extraction/scrub       Stripping Total for
                                                                    column             Column Exmriment
          inventory estimate using
          regressionmethods, g                                                  933        1148    2081
          Inventory estimate using
          Burkhrt        g                                                      932        1184    2116
          Dump value, g                                                         960        1090    2050
                                                           Exsmisnentsl Run 2D-2
                                                                Estrmtion/scrub        Stripping Totsd for
                                                                    column             Column Expiment

          Inventory estimate using
          regression methods, g                                                 1577       1298    2875
          Inventory estimate using
          Burkfsart      g                                                      1609       1304    2913
          Dumo value. g                                                         1430       1315    2745
46
                                                                 g


                                         X
                                 g
g                                                    g




         =       +   +       +       +       J


                 x




    PO                                                       q



             q           q



             o                                   q



             q



             0                                   .       q




    L        o           0                       s       q




                         q                               q
1




                                0

                                                                                27. Estimated profile-regression   methods.




                                              . .. .. .


                  . ..
           ”-’~




    mwm




                                                                                                         u-


                                                                                                                   u




    28. Estimated profile-Burkhart   model.




                                                          ,. ....”
                                                                     ...... ~       x




                                                             1
                                                                                                                         Of”%&
                                    x
                 . .. . . . .. .. . . . .. . .. . . .
             i

     ..x’”




                                                                                        29. Estimated profile-regression             methods.




                                                                                        x
                                                                                            ~
                                                                                    -           .. ..
                                                                                                              X
                                                                           ... ..                       ...
                                                                       .                                      ..            x
                                                                 ,..   ~                                           .
                                                                                                                       ..




                                                                                                                                ,x
30. Estimated protile-Burkhart                          model,




                                                                                                                                     e+w%!ik
                                                          Fig. 31. Estimated profile-regression       methods.




                                          o




            1                                  los
                                               aonou
                                              or COLUUN




                                                                                                  u




    Fig. 32. Estimated profile-Burkhart
                                                                                    o




                                                1                         ~                                m




r
        a

        a




                             a




    A
            a                                        1L
                                             a
                    4L
                                         A
a
            a                                            a

                                                 a


                a
                                 a

                                     A                       a




                         h
                                                     2
                                                               VACUUM




                                                                                Fig. 33. An isometric view of the precipitator
                                                                                         during solution transfer.




      w           ADU PRECIPITATIONAPPARATUS
     UO~(NO
      SOLUTION    (URANIUM SOLUTIONTRANSFER)




           An isometric view of the precipitator
          during ammonia addition.
                                                   METERING
                                                               /
                                                               r
                                                               /
                                                                        V4




                                                                                                   \

                                                    PUMP
                                                          o
                                                     @




                                                       1
                                                           .
                                                                   OH        ADU PRECIPITATION APPARATUS
                                                    .U,                          (AMMONIA ADDITION)
                                                   B




52
                                                            a

        a                       a                                   a

                            a                   a                   a




                        a                       a
                                                    a




                a
                                            a

            a       x               a                           a
A
            used                                        a
    a                                   a



                                        a
                    35. Detector assembly and its pedestal.


                                                   a
a                                                                     a
a

                                     a

                                                                  a
            a

A               a        (

        a
    a                                                         a




                     a
                                  PRECIPITATOR
                                  COLUMN




                                                                          /
                                                                  /
                                                          /
                                                 /
                SH ELDED
                DE “ECTOR
“ B“ ( - 15°)             -.


“               &


                                       \


                                           \

                                                 \

                                                      \

                                                              \
                                                                                       \
                                                                      \

                                                                              \


                                                              LEAD
                                                              SHIELD
                                                                                           4=
                                                                                           .




                                                                                  II

           36. Detector positioning in front of the precipitator for measurements          A and B.




                                                                                                      55
                      a
          a




    36,



a
                  a




              a
    a
                                             a




                                             a

                    3h
            a
                    h
        a       a
                                     3

                         a




                                 A
                                         C




                                             a




                             a



5
                                HOLDUP      OF          COLUMN
                                      FROFILE PRECIPITATOR
        n            \ 1            1            1         r               1            I       I




        1 -
    1                ‘“ \

3                                                      _
                                                                     -
                                                                   ............ .
                                                                                    -       \
6
             \                          - ....... ..
8                )

a                I                                             t
n
                 ‘ i’ “,.
Q       ;\
u
                     h ““.’...
E                           h      I                                      1             I
        o                   1      2            3      4                 5              6       7
                                                                        U

Fig. 37. Different profiles of ADU holdup along the precipitator column.




                                                  a
20


 0 }“’”           I          I           I           I           I           I
   o            20           4Q         60          80         100         120
                         -
     38. A comparison of inventory differences with NDA-measured total holdup.
                                                                                                           a



                                                                 a

            a


        +                 ,

                                                                                                  t=
                                  =         g


                                                            t
                                            a


a




                1.6           I       I         [     I         1     [       I      I       I 0       I
                      I
                1.4


                1.2


                  1



    4
    0
    x




                          u


                 0            I        I        I     I         1     I       I          1   I         I

                      0       5       10        15   20         25   30      35      40      45    50          55


                                      Fig. 39. Linear regression tit to calciner data.
                                                                                                             a
                                                                                      a

        a


    a

                                                                                                             a



            1.8              I           I    I     I      I      I       I      I        I    I


                                 u
            1.6




                1




                    tu                                                                                  1
            ‘“:~    O       5            10   15   20     25     30      35     40        45   50       ss
                                                           (kg
                                                   THROUGHPUT OF U)

                         Fig. 40. Application of Kalman filter to the feed dissolver data,




                                     a
    a

a

=           ,


                                                                                                    ~

                                                                                                                 61
                                                                        a



=   -


    t       t            -        –                                              a

        (                                                                                    a




                                                                                                               t=
                                      =     g
                                                                                 a




                                                                                                 a




                16

                14

                12




                8

                6

                4


                     t
                o            I        I      I      I       [       I       I        I       I       I    I
                     o       5        10    15     20      25      30       35       40      45      50   55
                                                  THROUGHPW

                             Fig. 41. Application of Kalman filter to filter funnels data.
    41
                                                     g
     g

                                                                          a                 $
                             a                                    +                     +

                                                         +
                                                         +    =
              +d
                                             a

     +   -         =~            .
                        +1

                             +   -                                                          a

                                                              +
         +     –         =       +   .


                                                                          d

                                                         t=                         g       a
                                                                                   t=       t
=                                                                 g
                                                                                            g

         t=         t=                                                a       t=




                                                 a


                                         a
                    1.8           I   I      [      {        I     I       I     I        1               I
                                                                                                              0
                          I
                                                                                                          a
                    1.6                                                                               u
                                                                                              o
                    1.4
                                                                                     uo           u
                                             u
                                                                                     u
                    1.2

                      1

                    0.8

                    0.6
                              00




                     0                                                                    I               I
                          O       5   10     15    20        25   30       35   40       ~            50          55
                                                          (kg
                                                  THROUGHPUT OF U)

                                      42. Changepoint model for the calciner data.



                     a                                                                        a
                     a


       =              , 0s ts 9


     t=9
           s ts

      t=
                                           t=                                        t=



                                                         a

                              a


                a                                                      a
            a




64
                                                                                                          a




                                                                   a
                  A



         t=
     a




t=


          80          1       I            I   u       I       i                   [        I    1    I       I


                                                                               u

                                                   a
                                       u




                                              u 0

                                           00
                                                           0



                                  uo                                   u

                              0
                      0                                                                00
                          u                                                o


              0       I       I            I           I       I                   I        I    I    I       I

                  o   5       10       15          20          25              30           35   40   &l      50   55
                                                           (kg
                                                   THROUGHOUT OF U)
                          43. Measurement history of holdup in the precipitator.




                                                                                                                        65
     80                   I       I              I    o     i         [          I




                                                 u
                      u




                              u


                  0                   /




              0
                          I       I              I          I         I          I
      o
          o               5
                                                   (kg
                                          THROUGHPIJ1’ OF U)

          44. A smooth curve superimposed on early portions of the precipitator data.




                                                                            9
                                                     0.72       ---        ---
                                                                            3




                          a




                                          s ts
                                                                                        t =
                                                                              s ts

                                                     t=




66
                                                  u



                            u

                                                      0           u



    0   I               I                I                I                   I

                                                                          5                  5

                                            (kg
                                    THROUGHPUT OF U)

        45. Application of Kalman filter to steady-state portion of precipitator data.




                                                                      a


a




                                                                                                 a
a

                                     a                                                   a

                                                              a




                                                                                         a




                                                                                                     67
                       a                            a                 a              m
                                                     a




/

                                                                          . .
                                                                        ... ...




    46. An isometric view of the stainless steel loop for uranyl nitrate solution.




      Fig. 47. An isometric view of the CPvC loop for uranyl fluoride solution.
                                    a
                     A
                             a




                                                          A




             a
                     a




                 A
                                                              L
                     a


             7




TABLE XV. Component Description snd Experimental
          Parameters of Circulation Loop
Components/      StnirrtessSteel
 Parameters           Loop                     Loop
Pipe, id.        1.9 and 2.5 cm         1.9 turd 2.5 cm
Lmp length       50 m                   50 m
Pump             Stldrdess steel        HasteUoy-C
                 gear pump              gear pump
                 Stairdess steel        HasteUoy-C
                 5                      6
                 1                      1
                 20
                 L                      2
Flow meters
                 .
                 L                      2
Storage tank     Polyethylene           Polyethylene
                 200.L capacity         200-L capacity
Surge tank       Polyethylene           Polyethylene
                 200.L capacity         2CS0-L capacity
Ftow             10 IJmin &             11 IJmin &
                 20                     22 IJmin
Uranium                                 91 g/L
                 as                     m
Excess acid      4 moles of HNC)~       4 moles of
                 mole uranium           mole uranium
Throwshout       59.5 t uranium              turanium
                                                                  69
                                                                                                 a
                                           A     x                                      a
                  a
                                                                          a
    A
                                                                              A




                                                                              v
        Fig. 48. Shielded NaI(ll) detector mounted on a long arm with a designed capability to
                 reproduce measurement locations on the solution loop.




a
                                                         a
                                                                   a
            a
    a




A
        a




    6
                4       2


        A




        t


=   +


                    ~




            6
        =           +       i=



                =       –        .

                                                                 A
                                                         –


            a



                                                     B
                                     a




                                         a

                                             a
                                                                     a




                                                             a
                                                 a
                                                                     a
I


    a
                      I              [       I         I       I            I        I           I           !
                         MATERIAL

                         u
                                                                                                 0
                                                                        0            0
                                                                                                         0
     9                                                         0
     L
     0
                                                       0
                                 0       0

     I
                     0
                                                                                                     0
               0                                   0
                                 u
                         u               u                          u
                                                                                 u
                                                                                             o

                 u


         0                           I       I         [       I             I       I           I           I

             O       5           10      15         20         25           30       35          40          &   50
                                                         (103
                                                 THROUGHPUT kg OF U)

                     Measurement history and filtered values for pumps at low flow rates.



                             I           I                 I            I                I               I

                         MATERIAL

                         Oss
                         o CPVC




         0 I                 I           I                 I            1                I               I

                                                                                                                 110
                                                         (103
                                                 THROUGHPUT kg OF U)

         Fig. 50. Measurement history and filtered values for pumps at high flow rates.




74
  1             I        1     I      1       1      1       I      1       I       I
               LOCATION


                   u7
0.8                010




0.6




 0
      o       10         20   30     40     50      60     70      80     90        100 110
                                           (103
                                   THROUGHPUT kg OF U)

          51. Measurement history and filtered values for stainless steel unions.



  1            I         I    {       I      I       i      I       I      I        1
               LOCATION

                 L&
                 0107
0.8              0 lto




0.6




 o
          AB&                                      ~        I       I      I        I
      0       10     20       30     40     50     60      7(I    80      90
                                           (103
                                   THROUGHPUT kg OF U)
      Fig. 52. Measurement history and filtered values for CPVC unions.




                                                                                              75
 3                I       I       I      I      I         I     I       I      1         I   I
                  LOCATION
                     IN
                       LOOP
2.5                    n3
                       015
                       AV

 2


1.5


  1

              o




 0
      0
          ‘*.     10     20       30     40
                                                I

                                               50
                                                          I

                                                         60
                                                                1

                                                               70
                                                                        I

                                                                        80
                                                                               {

                                                                              90
                                                                                         1

                                                                                       100 110
                                               (103
                                       THROUGHPUT kg OF U)

                   Measurement history and filtered values for stainless steel valves.



  3 I              f       I       I      I      I        I     1       I      I         I   I

2.5


  2


 1.5


      1




          I                                                             u          .
  0b               I          1    I      I         I     I     I       I                I   1

   0              10      20      30     40     50       60    70       80    90       100 110
                                       THROU(WW         (103 kg OF U)

                         Measurement history and filtered values for
     1      {             I    I       I               r“       I       I        I        I       I
            LOCATION

                L&P
                04
0.8
                A   13



0.6

                                                                                                  A


                                                            A




                                                            0
                                                                                      n
 0                                                 I            I       I    I        I

      0    10        20       30     40        50           60      71)     80       90       100 llo
                                           (105
                                   THROUGHPUT kg OF U)
  Fig. 55. Measurement history and filtered values for stainless steel pipes.



  1         I            I    I       I        I            I       I       [         I       1




                      0

                                           o


 0                                             I            I       I                         1

      0   10        20        30     4.0 50                 60      70      80       go
                                            (105 kg OF U)
                                   THROUGHFIJ
          56. Measurement history and filtered values for                        pipes.
           1           I            I        I         I    [        I    I    I     1    I
                       LOCATION


                            u5
     0.8                    09
                            A 11
                            01.1




       0
               0       10          20        30        40   50       60   70   813   90
                                                          (103
                                                  THROUGHPUT kg OF U)

               Fig. 57. Measurement history and tiltered values for stainless steel elbows.



           1            I              I      I         I       I     I    t    I     I       1   I
                        LOCAllON
                                L&
                                IJ 105
      0.8                       0109
                                Alll
                                o114


      0.6




                                                  Ii




                                                            0


                            I            I    I         I       I     I    I    I     I       I   1
           0
                   0    10           20      30        40       SO   60   70   80    90   100 110
                                                          (103
                                                  THROUGHPUT kg OF U)

                       58. Measurement history and filtered values for CPVC elbows.




78
     1           I           I    I      I        I    I       I      1       I        I
                LOCAllON
                      LO!$
                      u2
0.8
                      A16



0.6




 0              I            I    I      I       [     I      I       I      [         I

      o        10           20   30     40       50   60
                                                       —
                                                             70     80      90     100     110
                                              (103
                                      THROUGHPUT kg OF U)

          Fig. 59. Measurement history and filtered values for stainless steel tees.



  1              I           I    1      I        I    I       I      I       I        I
                    LOCATION
                       IN
                      LOOP
                     u 102
0.8                  0 IIZ
                      A




0.6




                                             0


                I            I    I      I        I    I      I       I
 0                                                                           I         I

      o        10           20   30     40       .50 60      70      80     go
                                              (103
                                      THROUGHPUT kg OF U)

                     60. Measurement history and filtered values for CPVC tees.




                                                                                                 79
                                A
                            a



                                    a

                        a
a




                                        5   6




    1




                    a
        a   a                                   a
                a                               a
                                            a


    a
                                    a
                                            a


            a




                                            a
a
        a

a




                C
                                a

                                            a
                    a
                            a
                                        a



                        a




                                                81
                                        a




a


    a
                    A


        a




                a           a       A


            a




                    a




            a           a       a

a
     =
tiikes               =&
                              a
a
                          a


                                          a
                                      a
                 A


                              a




             A




                                              a

                                  a
         a
             a

     a           a                           a




         a                   a




                     a               a




                                 a




                             a
                                                 a




                                         a
                         A




84
             a




     a




                 a
             a

                     a




         “
         m



4.
             1


             1
7.




      “




              a


          a




20.
    a   a


A




“




            87
     “




88
                                           APPENDIX A


                      USE OF TRACERS IN MATERIALS HOLDUP STUDY

                                            K. K. S. Pillay


I. INTRODUCTION

    Holdup measurements are generally based on the concept of dividing processing facilities into
 contiguous collection zones and performing NDAs to estimate residual inventoriesof SNM. Often
 nondestructivemeasurementsfor holdupare attemptedusingpassivegammaor neutronassay techniques.
This approach generallyencountersdifficulties   caused by facility-and process-relatedproblems,whichin
 turn compoundthe inherentlimitationsof passivegamma assay techniquesfor the measurementof SNM.
 Some of the importantlimitationsof passiveassay techniquesfor the measurementof enricheduranium
 and plutoniumare
                                                      ~d
    1. the low specificactivity of the isotopes ZS5U zJ9puand the accompany~g difficultiesin the
       measurementof smallamountsof uraniumor plutoniumin the midstof largebackgroundradiations
       from other parts of an operatingplant,
                        of
    2. the insensitivity passiveneutron assay techniquesfor the detectionand measurementof residual
       amounts of uraniumor plutonium,
    3. the dominanceof self-attenuationin the matrix of the SNM and the attenuation by construction
                                                               and
       materialsof the low-energygamma radiationsfrom 23SU 239Pu, and
   4. the potentialvariabilityin the distributionof uraniumholdupwithinthe processequipmentand the
       consequentmarginalvalueof conventionalcalibrationtechniques.
   The limitations of NDA techniques are recognized, and Regulatory Guide 5.13,A-1in describing
physicalinventoryproceduresthat are acceptableto regulatorystaff, discussesthe acceptabilityof other
methods such as “tracer or step function inventory” for dynamic inventory development.One of the
uniquemethodsof overcomingthe limitationsof passiveNDA techniquesis the use of a tracer to account
for the residualSNM. Safeguardstechniquesand process inventorydeterminationsusing minor isotope
techniqueshave been previouslyreported.A-2. A-3 other suggestions    on the potential use of radioactive

tracers in materialsholdupmeasurementsA-4nd for the study of materialsflowin a largefuelsmaterials
                                              a
preparation plantA-3   have been made in the past. However, there are no known reports on the use of
tracers for the measurementof holdupof SNM for materialsaccountabilitypurposes.Amongthe various
typesof tracers that are in commonuse,a radioactivetracer that is compatiblewiththe systemis the most
desirablefor passiveNDAs.
                                                                                                  in
   Tracers are powerfultools in the study of process kinetics,and they have been used extensively the
investigationof biological,geological,environmental,and chemical systems. In several experimental
studiesof this programto measurethe holdupof uranium,radioactivetracers wereused in equipmentand
facilities used in the preparation of nuclear fuel materials. The use of radioactive tracers in these
experimentsofferedconsiderableadvantagesto measuringuraniumholdupand its variationsas a function
of throughputand somechosenprocessparameters.Such tracer applicationscan be ofvalueto measuring
holdupof both uraniumand plutoniumin productionfacilitiesof nuclear materials.


II. EXPERIMENTAL STUDIES USING TRACERS

  One of the importantaspectsof the research study reported here was an attemptto developestimation
modelsfor materialsholdupat HEU-processingfacilities.An integralpart of this programwas to conduct
specially designed experimental studies on several unit processes common to industrial operations
                                                                                                           89
     involvingthe preparation of HEU nuclear fuels.These experimentswere conductedto collectdata for
     developingholdupestimatorsthat are equipmentand processspecitic.Three of the experimentsin which
     radioactivetracers were used to measurethe amountof uraniumholdupare
        1. a dust-generating operationat a HEU-processingfacility,
        2. an ADU precipitationand calcinationprocess,and
        3. a solutionloop systemcirculatinguranyl solutions.
        The first experimentinvolvedthe study of uraniumholdupduring a dust-generating    operationin which
     two types of uranium oxide powderand one type of incineratorash containinguranium were used.The
     experimentalfacilityconsistedof a glovebox, someductwork,and an exhaustair filtersystem.The total
     throughput of uranium through this experimentalfacilitywas -1 kg/cyclefor a total of 70 kg for seven
     experiments.Detailsof this experimentalstudy werereportedin Sec. III.
        The second experiment,detailedin Sec. V, consistedof the precipitationof uranium as ADU from a
     uranylnitratesolution,filteringout the ADU, and calciningit into U308.The precipitationprocesseswere
     carried out in a large,cylindrical,stainlesssteelvessel.The filteredADU was calcinedin Inconel-600trays
     in a Lindbergfurnace.The throughputof uraniumthroughthis systemwas -1 kg/batchwitha cumulative
     throughputof-50 kg.
        The third experiment(seeSec. VI)consistedof circulatingtwo typesof uranylsolutionsin two separate
     loops,one builtof stainlesssteeland the other fabricatedfrom CPVC. The loopswerebuiltto incorporate
     large storage tanks, circulationpump(s),pipesof various dimensions,elbows,tees, unions,flowmeters,
     valves,and terminalvalves.One of the solutionspumpedthroughthe stainlesssteelsideof the loopwas a
     uranylnitrate solutioncontainingexcessHNOJ (4 molesof acid per moleof uranium);the other solution,
     circulated through the CPVC side of the loop, was a uranyl fluoride solution containing excess
     hydrofluoricacid.The total throughputthroughthe systemwas equivalentto -110 tonnesof uraniumat
     a circulationrate of-50-100 kg/h of uranium.
        The objectivesof these experimentsincludedperiodicmeasurementsof the residualuranium in the
     system and attempts to correlate throughput with holdup. In the early stages of designingthese
     experiments,it was realizedthat it wouldbe impracticalto make the necessarymeasurementsfor these
     experimentsby attemptingNDA of 23SU u5ing scintillation         gamma assay techniques.The quantitiesof
     materialsto be measured during the experimentsranged from few tenths of a gram to a few grams of
     uranium in large process vessels and equipment.The changes in the quantitiesof holdup of uranium
                                                                    o
     betweenmeasurementswereevensmaller,and the difficulties f measuringsuch smallamountsof material
     in experimentalfacilitieslocatedin processingareas were not trivial.


     A. Qualitiesof a Tracer

        Some of the desirablequalitiesof a tracer for processholdupmeasurementsare the following.
        1. A tracer should have unique characteristicsthat would make it easily identifiablein a very large
           matrix.In the case of radioactivetracers, this qualityis generallyachievedby the uniquenessof the
           radiationsemittedand ease of detectionand measurementusingsimplemeasurementtechniques.
        2. The tracer must be physicallyand chemicallycompatiblewith the system and the process under
           investigation.This is generallyaccomplishedby choosinga distinguishable     isotopeor a chemical
           analogueof the elementthat willfollowthe major componentof the systemthroughoutthe process.
        3. The tracer must be in extremely small concentrationsso that it will not influencethe process
                                                                        T
           chemistryor the product of the processunder investigation. racers in concentrationsof parts per
           millionor less wouldsatisfythis requirement.
        4. When a radioactivetracer is used,it wouldbe desirableto choosea radioactiveisotopeof relatively
           short half-lifeso that the radioactivityoriginatingfrom the tracer would soon disappearfrom the
           matrix after the usefuldurationof the experimentalstudy.
     These above-mentionedqualitieswere chosen as criteria for the selectionof tracers in our experimental
     studies.
90
    B, Tracers Used in HEU HoldupMeasurements

       In experiment1, neutron-irradiatedsamplesof (a) powdereduraniumoxideand (b) an incineratorash
I   containing-10 wtvo of uraniumoxidewere used as tracers. These sampleswereirradiatedin a research
    reactor until- 1O’s fissionswereintroducedin the tracer sample.The sampleswereallowedto coolfor -2
    w,:eks to reduce the 1evelof short-livedfission products and to maximizethe level of 9sZr-Nb.In
    experiments2 and 3, a chemicalanalogueof uranium,with a uniqueneutronactivationproduct,was used
    as a tracer. This isotope,4%c,was produced by neutron activationof natural scandiumas SczO~.The
    propertiesof theseradionuclidesrelevantto these tracer applicationsare summarizedin Table A-I.
       The gamma emissionsper unit time per unit weightof the radionuclidesin Table A-I show that the
    specificactivityof the tracer nuclidesis -11 orders of magnitudehigherthan that of IOOVo-enriched 23SU.
                                                                              advantagefor the tracers 100
    If the tracer nuclidelevelin uranium is 1 ppb, there is a specific-activity
                               In
    tiInesbetterthan for Z3SU. addition,the higherenergygamma emissionsfromthe Vacersin the range‘f
    0.5-1.2MeV minimizesthe interferencesfrom beta and low-energygammas.Thus, the overalladvantage
    of usingthese tracers at the part-per-billionlevelfor uraniumholdupmeasurementcan be at leasttwo or
    three orders of magnitudebetterthan the directNDA of 23SU.                         can
                                                                  Further improvements be accomplished
    by usinghigherlevelsof tracer and tracers with higherspecificactivities.
       Physicaland chemicalcompatibilityof the tracer with the uraniumsystemis essentialto the successful
                                                                                           t
    functionof the additiveas a true tracer for uranium.Through carefulexperimentation, he chemicaland
    physicalformsof the tracers for three experimentsdescribedherewerechosen.TableA-II listschemically
    and physicallycompatibleforms of the tracers that wereprepared and incorporatedinto the experimental
    systems.The tracer levelswere monitoredat variousstagesof the processesto assure homogeneityand
    performanceas a true tracer for uranium.Carefullydesignedbench-scaleexperimentswere performedto
    ccmfirmthat the tracer chosen followeduranium quantitativelythroughoutthe process.The analysesof
    uraniumwas performedusingdestructivechemicalassay techniquesdescribedin Sec. V.E. Scandium-46
    tri~cerin the system was measured using a well-shielded     7.5- x 7.5-cm NaI(Tl) detector and a single-
    channelanalyzer system.


                         TABLE A-I. SpecificActivitiesof 23%J nd Tracer Isotopes
                                                            a
                                                  Prominenty’s      y-Emissions
                         Nuclide     Half-Life       (keV)          “(s-l g-l)
                         235u
                                   7.04 x 108yr        185.7         4.32 X 104
                         46sc
                                    83.85 days         889.3         2.5 X 1OIS
                                                      1120.5
                         9sZr-Nb 64.4 days             724.2         1.56 X 1OIS
                                (31.15 days)           756.7
                                                       765.8




                                                                                                               91
          TABLE A-H. Tracers and Their CompatibleForms
          Experiment                  Tracer              PhysicalForm                Chemical Form
          UqOgdust                    Fission             Solid(particle              In situ-gen-
          generation                  products:           size same as                erated fission
                                      9~Zr-Nb &           U308)                       products in
                                       ~40Ba.La                                       U308
          ADU precipitation           46SC                Solutionto                  SC3+,
          & calcination                                   solids (changed             SC(OH)J,and
                                                          with uranium)               SC203
                                       46sc                                           SC3+
          Uranyl nitrate                                  Solution
          solutionloop
                                      46sc
          Uranyl fluoride                                 Solution                    [ScF6]3-
          solutionlooD



     C. Limitationsof ExperimentalFacilities

        The holdup experimentswere conducted at two facilitieswith large inventoriesof uranium and/or
     thorium.FiguresA-1 and A-2 illustratethe nature of the interferencesby the backgroundradiationsat the
                                                                  ~d
     two facilities.FigureA-1 showsthe gammaspectrumof ISZTh its daughters,whichwerethe dominant
     background at the facilitywhere the dust-generationexperimentwas conducted.In this illustrationthe
                               was
     gamma spectrumof 2MU insertedto showthe relativelocationof the most abundant Primary %amma
     peak from enriched uranium. Also included in this illustrationis the gamma spectrum of a 95     Zr-Nb
     equilibriummixture,which was the dominantactivityof the tracer used.The gamma radiationsfrom the
                                     a
     tracer are clearlydistinguishable nd measurablein the midstof largebackgroundradiationsfromthorium
     and its decay products. Similarly,Fig. A-2 showsthe backgroundradiationsat the uranium-processing
     facilitywhere experiments2 and 3 were conductedusing 46sc a5 the radjoactjve    tracer. Here again, the
                         as
     advantageof using4’%c a tracer for the NDA of uraniumis obvious.


     D. Tracer Levelsand MeasurementMethods

       The amount of radioactivityof the tracers used in theseexperimentsrangedfrom 1to 3 x 109Bq/kgof
     uranium.For 4%c,this amountedto an atom ratio of-1 tracer atom to 109atoms of uranium.
       The instrumentationused in these measurementsconsistedof a shieldedNaI(Tl) scintillationdetector
                          a
     and a single-channel nalyzerand a scaler.With these instruments,it was possibleto quantifyaccurately
     the tracer levelsin the residual uranium holdup without undesirableinterferencesby the background
     radiations.




92
     100                                                   I           I     I         I
                                                                           —2321H
      90                                                                   —-   &.3g
                                                                           .........
                                                                           —— 95W
      80




                                                    I
                                                    I
                                                    I
      20
                                                    I
      10
       o“
            0       200       400          600
                                                    L
                                                  800 1000 1200 1400 1600 1800
                                                      (Kev)
                                                 ENERGY
Fig. A-1. A                Of g       of‘Jzl%           23SU,
              combinationthearmna-spectra anditsdaughters, andthetracer
            nuclide
                  9sZr-Nb.



     100

     90                                                                    =-”2
                                                                           ..... ..
     80

      70
                                                                ,..:
k    60
E’
—    50




                               ...,
                               .,,
                             ------,,
                                 ~
                                ,.
     40

     30

     20

      10            #
                              -------
                             -k :;                       ,,p
       0
                v       ‘k                                         -‘~
            o       200       400          600   800    1000 1200 MOO                1600 1800
                                                 ENERGY
                                                      (Kev)

Fig. A-2. A combination      of the gamma-spectra   of natural and/or low-enriched   uranium,   23’U,
            and
              tracer    nuclide   46 SC.




                                                                                                        93
     III. RESULTS AND DISCUSSION

     A. Homogenizationof Tracers in UraniumMatrices

        The incorporation of a tracer in a homogeneoussolution of uranium is generally easier than the
     introductionof the tracer in a solidmatrixas withthe U30~dust-generation experiment.In thislattercase,
     ~200 mg of U~08 (or ash containingUJOJ were irradiated in a neutron flux to generate the fission
     productswithinthe matrixof UjO~.The activeUJO~(or ash)wasthenblendedwiththe bulkmaterial.The
     mixture was sampled and counted to assure homogeneityof the tracer within the UJO~matrix. The
     blendedmaterialwas consideredhomogeneousif the relativestandard deviationof the specificactivityof
     the sampleswas ~5V0.
       The uranyl nitrate and the uranyl fluoridesolutionsused differentionicforms of scandiumbecauseof
     the chemicalcharacteristicsof the media.Homogeneousmixturesof the uranylsolutionsand correspond-
     ing tracer forms were prepared and preservedfor up to 2 months in containersmade of the the same
     materialsused in the experiment.These mixtureswere periodicallyanalyzed to determinethe potential
     segregationof tracer fromthe uraniummatrix.It was determinedthat the uranylnitratesolutionwithSC3+
     ion was compatiblewith the polyethyleneand stainlesssteelloop and the [ScFb]3-ion in uranyl fluoride
                                           and
     was compatiblewith the polyethylene the CPVC loopwith a hastelloypump.
        In the case of the ADU precipitationand calcination,the uraniumwentfroma homogeneous    solutionto
     a precipitateand then to a calcinedsolid.The tracer scandiumalso followedthe physicalchangeswith
     concomitant chemical changes. The basic chemical reactions of uranium and scandium during this
     experimentare as follows:
        UOZ(N03)Z+ NH, OH ~ precipitation~ (NH4)ZUZ07              oXHZO

       (NH4),U,0, e calcinatione U30,

       U30~+ HN03 -+ dissolution~ UOZ(NOJ2           ; and

       SC(NOJJ+ NH40H e precipitation+ SC(OH)3

             +
       SC(OH)J calcination~ SCZ03

           +
       SCZ03 HN03 -+ dissolution+ Sc(NOJq.

     Carefulmeasurementsmadeof the movementof 4%ctracer withuraniumshowedno partitioningbetween
                                            p
     uraniumand scandiumduringdissolution, recipitation,and calcinationprocessesnor duringrecyclingof
     the products in the same processes.Some of the typicalresultsof the quantitativemeasurementsof tht
     movementsof “%ctracer duringvariousstagesof ADU precipitationand calcinationare shownin Tabh
     A-HI. These measurementsindicatethat scandium,a chemicalanalogueof uranium,is an excellenttrace
     for uraniumduringthe transformationsinvolvedin this unit process.


     B. NDAs and CleanoutMeasurementsfor HoldupDetermination

                                                                                 to
        A numberof cleanoutmeasurementswereperformedduringthis investigation comparethe resultsof
     NDAs usingthe radioactivetracers. The cleanoutmeasurementswereperformedby a varietyof methods
     for the various experimentsreported here. Among the analyticaltechniquesused were isotopedilution
     mass spectrometry,titrimetry, spectrophotometricanalysis using Arsenazo-HI, and gamma-ray spec-
                                                                                           high-efficiency
     trometricmeasurementsof the tracer activityin the cleanoutmaterialusinga well-shielded,


94
                          TABLE A-III.            Per Cent Tracer Found at Various Stages of
                                                  ADU Precipitation Catcination
                                                                   ccrd
                          State of Uranium              State of “%c           Per Cent of Initial
                             in the Matrix                 Tracer                      spike

                          U02(N03) solution             *3+                           100
                          ADU                           SC(oH),                        97.9
                          U,05                          SC*O,                          98.1
                          U30S recycled      to

                          ‘02(N03)2                     w+                             98.7
                          Reprccipitation     m
                          ADU                           SC(OH)3                        96.8
                          Recalciruttion to
                          U,08                          SC203                          97.1




        d
Ni~I(Tl) etectorcoupledto a multichannelanalyzer.In Table A-IV, the resultsof someof thesecleanout
measurements are compared with the correspondingvalues of NDA measurementof tracers in the
residualholdup.

                     TABLE A-IV. Comparison of NDA Measurements of Holdup with CIearsout
                               Mccsuremcnts (in Ormrrs of Uranium)
                        Experi-        Equipment/                 Tracer NDA              CleurOut
                       mart No.            Psrts                  Memzrsmcnt             Messuremcnt
                          1                                            3.S6                   3.s9
                                       (fuze U, O,)                    6.22                   5.10
                          1               Ductwork                      1.66                  1.06
                                          (ash with                    2.50                   2.51
                                            U,o,)
                          1               Ductwork                     1.60                   1.89
                                             (coarse
                                             U,o,)
                          2           ADU precipi-                     12.6                   14.6
                                      tation vemd                       9.3                   10.2
                          2                 Cdcicdng                    1.7                    1.5
                                             furnace
                          2                 Cslcinlng                   1.4                    1.3
                                              traya
                          3             Pipes (per                     0.37                   0.40
                                             meter)                    0.16                   0.15
                          3                  Elbows                    0.02                   0.03
                                                                       0.03                   0.03
                          3                  Vdvc!                     0.40                   0.37
                          3                   Tees                     0.08                   0.07
                                                                       0.08                   0.08
                          3                  Pumps                     13.7                   11.9
                                                                        9.4                    7.0




   The results of these experimentalstudiesclearly demonstratethat the sensitivityof holdup measure-
ments can be significantly improvedby thejudiciousincorporationof trace levelsof radionuclideswith a
highspecificactivityand desirablegamma-emission   characteristics.This approachis particularlyvaluable
                                                                                       h
in generatingdata for the developmentof holdupestimatorsand in determiningsignificant olduppatterns
of large processingfacilitiesof SNM. The cleanoutmeasurementsof materialsholdupnecessarilyinvolve
major disruptions in the operations of the facilitiesand considerableinvestmentof manpower and
resources. The NDA measurementsdescribed here using tracers can be performed in a few minutes

                                                                                                         95
     without any significantdisruptionsto facilityoperations.Further, the data presentedin Table A-I and
     Figs. A-1 and A-2 clearlydemonstratethat the passiveassay of the gamma radiationsfrom the 23SU   for
     the study of holdup in these experimentswould have been futilebecause of the extremelylow specific
                    and
     activityof 23SU the overwhelming    interferencesby the backgroundradiationsresultingfromthe large
     inventoriesof uraniumand/or thorium.


     REFERENCES

     A-1. RegulatoryGuide 5.13, “Conduct of Nuclear MaterialPhysicalInventories,”US Atomic Energy
          Commission(November 1973).

     A-2. “Evaluationof Minor Isotope SafeguardsTechniques(MIST) in Reactor Fuel Reprocessing,”US
          Atomic Energy Commissionreport WASH-1154(February 1970).

     A-3. D. E. Christensen,R. A. Ewing,D. P. Gaines,Jr,, R. Kramer, R. A. Schneider,L. A. Stieff,and H.
          Winter,“A Summary of ResultsObtainedfrom First MIST Experimentat Nuclear Fuel Services,
          West Valley, New York,” in Sc#eguards Techniques, Proc. Symp., Karlsruhe, July 6-10,1970
          (InternationalAtomic EnergyAgency,Vienna,1970),Vol.I.

     A-4. T. Gozani,“Reviewof Evaluationof HoldupMeasurements,”Nucl.Mater.Manage.VI(3),424-433
          (1977).

     A-5. R. S. T. Shaw, “The Investigationof Industrial Plant Process Using Radioactive Tracer,” J.
          Radioanal.Chem. 64, 337-349(1981).




96
                                           APPENDIX B

                   PRINCIPLES OF REGRESSION AND KALMAN FILTERING

                                            R. R. Picard

I. REGRESSION

   A brief developmentof estimates based on regression methodologyis presented in the following
paragraphs. Such estimatesare used in the analysesof the dust-generationexperimentsand of the liquid-
Iiquidextractionpulse-columndata, A more detailedtreatmentof the resultsgivenbelowcan be foundin
many textsB-l*B-2 regressionand linearmodelstheory,includingseveralcitedin the referencelistof this
                on
report.
  The standard linearmodelrelatesa “dependentvariable”y to p “explanatoryvariables”{~}by

  Y = ml    + P2X2+ ,.O~pxp + e,                                                                (B-1)

             a
wherethe {~1}re unknownparametersand e denotesthe error in measurement.Onceparameterestimates
    h
{f~i}ave beenobtained,predictedvaluesy of the dependentvariabletake the form

  ; = 01%   +     +...+
                132X2 ppxp.                                                                     (B-2)

Severalexamplesof Eq. (B-2)are givenin previoussectionsof this report. Data from the air filtersusedin
the dust-generationexperimentsconformedto the model(writtenin the notationof Sec. III)

  fif (t)=     ,
         ii+ ptz

wherethe dependentvariableh~t)is the amountof holdupon the filterat throughputt and dependson the
explanatoryvariablest and t2.A secondexample,also taken from Sec. III, concernsthe modelingof the
glovebox floor,wherethe estimateddensity~(t,x,y)of materialat location(x,y)on the floorwhenprocess
throughputis t is



As is apparent from inspectionof Eq. (B-l), far more complexrelationshipsmay also be examinedusing
linear modelstheory.
   The procedure for using observed data on the dependent variable and explanatory variables for
                                          in
purposesof estimatingthe parameters {~i} Eq. (B-1) is straightforward.The basicideais to obtain {~1}
such that the fittedEq. (B-2)agrees“best” withthe observeddata. Often“best” is in a least squaressense
as the resultingestimateshave desirablepropertiesfor the common situationwhen errors are approx-
imately normally distributed.Standard statisticalcomputerprograms contain least squares routinesfor
this reason. For completeness,however, it should be noted that other notions of “best” could be
considered,leadingto eitherweightedleast squaresor to robust estimation.
                                                         i
   Derivationof the least squaresparameter estimates{~1}s mosteasilyaccomplishedin compactmatrix
notation. Let y be the vector of observedvaluesof the dependentvariable,each valueconformingto Eq.
(B-1)for its associated{xl}.For ~ the vector of unknownparameters {~l};~,the vector of measurement
errors; and X, the “designmatti% of constantsof the linearrelationship;the modelis

 ~ = Xfi + e .
       .-


                                                                                                         97
     The least squares estimate of ~ is

       } = (x’x)-’     X’y ,

     and predictedvaluesare obtainedas indicatedin Eq. (B-2).


     II. KALMAN FILTER

        The developmentof filteredestimatesis describedin the followingparagraphs.To facilitateapplication
     of this methodologyto problemsbeyond the steady-statemodel discussedin analysisof the ADU and
     solutionloop experiments,the Kalman falteris presentedin its generalform. For additionalinformation,
                                    B-4
     some elementaryreferences ‘“31 are provided.Also, the early developmentof filtering,largelypursued
     in the engineeringliterature,may be consulted.
        The objectiveis to estimatethe continuallychanging“state” of a systembased on noisy data. In the
     text, the state is simply the unknown quantity of holdup in a piece of equipment,and the relevant
     measurement history comprises the data, The model is represented by the measurement and state
     equations.In general,the measurementequationis written

       x(t)= m(t)h(t)+ e(t) ,                                                                              (B-3)

     where the measurement(s)x(t) and state(s)of the system h(t) at time t may be vector valued.The error
     vector e(t)is assumedto be distributedwith mean zero and covariancematrixr(t), and the “measurement
     matrices” {m(t);t = 1, 2, ...} are presumed known. Equation (15) of the text’ssteady-statemodel is a
     specialcase of Eq. (B-3)abovewith x(t) and h(t) scalar valuedand m(t) s 1, r(t) s ~.
       The state equation,in generalform, is

       h(t)= s(t - I)h(t - 1)+ c(t - 1)+ ~ (t - 1)                                                         (B-4)

     and relates the state of the systemh(t) at time t to the state h(t – 1) at time t – 1. The “state transition
     matrices” {s(t)}and “control vectors” {c(t)}are presumedknown,and @t)is distributedwith mean zero
     and covariancematrixq(t).Further, e(t)and e(t) are uncorrelated.Equation(16)of the textcorrespondsto
     Eq. (B-4)with s(t) s 1, c(t) s O,and q(t) - o;.
       The recursiveprocedureknownas the Kalman filterformallyproceedsas follows.
       1. Let h(l) be an estimateof the initialsystemstate h(1) and have covariancematrix v(l). Set t = 1.
       2. The state estimateat timet + 1 based on all informationthroughtimet is

           fi(t1)= s(t) fi(t)+ c(t) ,
             +

           and the error of predictionhas covariancematrix

           p(t + 1)= s(t) v(t)s(t)’+ q(t).

        3. The gain matrixis definedby

           g(t + 1)= p(t + I)m(t + 1)’[m(t+ l)p(t + I)m(t + 1)’+ r(t)]-’ .

        4. The state estimateupdatedfor the measurementat timet + 1 is

           fi(t+ 1)= fi(t+ 1)+ g(t + l)[x(t + 1)- m(t + I)fi(t+ 1)]

98
     and has covariancematrix

     v(t + 1)= [1– g(t + 1)m(t + 1)]p(t + 1),

  5. The recursioncontinuesby repeatingsteps 2-4. Propertiesof the falteredestimates{fi(t);t = 1,2,... }
                                       B
     can be foundin standard references. -3t0E-c

  In a finalnote, it is also possibleto obtain “smoothed”estimates.In contrast to filtering,in whichthe
current state of the system is estimated based on present and past information,smoothing uses all
availabledata to estimateall systemstates.Thus, a previousfilteredestimatecan be updatedbased on the
collection of subsequent data. Because smoothed estimates are not overly useful for near-real-time
accounting,the subjectis not discussedhere.


REFERENCES

B-1. N. R. Draper and H. Smith,Applied     Regression Analysis,   2nd Edition(John Wileyand Sons,Inc.,
     New York, 1981).

B-2. S. Weinberg,   Applied Linear Regression   (John Wileyand Sons,Inc., New York, 1980).

                                         “
B-3. R. J. Meinholdand N. D. Singpurwalla, Understandingthe Kalman Filter,”AmericanStatistician
     37, 123-127(1983).

B-4. E. J. Wegman,“Kalman Filtering,”in Encyclopedia ofStatistical     Sciences, N.   Johnsonand S. Kotz,
     Eds. (John Wileyand Sons,Inc., New York, 1982).

B-5. D. B. Duncan and S. D. Horn, “Linear RecursiveDynamic Estimation from the Viewpointof
     RegressionAnalysis,”J. Am. Stat. Assoc. 67,815-821 (1972).

B-6. D. J. Downing,D. H. Pike, and G. W. Morrison,“Applicationof the Kalman Filter to Inventory
     Control,” Technometrics22, 17-22(1978).




                                                                                                            99
                                              APPENDIX C

                DETAILED DATA FROM CONTROLLED EXPERIMENTAL STUDIES

        Note: The numberof significantfiguresin the data tabulatedin this appendixis not representative
      of the accuracy of modelingestimates.The relativeerrors of estimationsmay be evaluatedfrom
      estimatedvaluesand systemlossescomputedfrom measurements.



                          DATA FROM EXPERIMENTAL STUDY OF
                     URANIUM HOLDUP IN A DUST-GENERATING FACILITY
                                 (TablesC-I through C-XV)




100
                                                                                     —
 TABLE C-I.        Susnrnmy of Modeting Results for Msdium-Airflow Experi-
                   ment with U,O,

                          Measurement                           Estimated
                                                                       Holdupc
 Component                  Points”           Modelb                      (R)
 Glove InTxsi&s               1-2       6,(t) = o                     0
 Glove box floor              3-5         = 0.1617t
                                        6Jt)                           1.617
 Vertical segment             6-7       fiJt) = o.o173t               0.173
 FirstXJW
     d                         8        6,(t) =o.oo67t                0.067
 Segment txtwcm
   eltsows                     9        fib(t) = 0.0126t              0.126
 Second elbow                  10       fi,(t) = 0.005%               0.059
  Horizontal
    segment                  11-13      fib(t) = 0.0361t              0.361
 Filter                        14       IiJt) = o.0545t               0.704
                                              + 0,0016t2
 System totat                 1-14      fi(t) = 0.2948t               3.107
                                               +41.0016t2
 System weight
   loss                                                               3.198
 %ee Fig. 6 for details.
 %e fiction 6...(t) rsprssems tieestiatdhoIdup         *tie       h&tidud component
 when tbe throughput wss tIdlogmns.
 %ouchmzt       = 10 km.




TABLE C-H.                  Modeling for High-Airfiow Experiment
                   Summary of    Results
                      U,O.
                   with
                          Measurement                                      Holdupc
                                                                    Estimated
Comvonent                  Points’             Modctb                           (R)
Glove box sides              1-2                   =
                                              6,(t) O                            o
Glove box floor              3-5             $(t)= 1.582
                                                    +0.1 lo2t                   2.684
Vertictd segment             6-7            &(t) = 0.9276t                      0.287
   elbow
First                         8             Ii,(t) = O.olodt                    0.106
     b
S@mentetween
 elbows                      9             fib(t) = o.0203t                     0.203
Second elbow                 10             Ii,(t) = o.olo9t                    0.109
Horisontat
  segment                   11-13          fih(t) = o.0528t                     0.528
Filter                       14             lqt) = o.1544t                      2.301
                                                 + 0,0076tz
System total                            fi(t) = 1.582 + 0.3879t                 6.218
                                                  + 0.0076t2
System weight
  loss                                                                          6.204
%= Fig. 6 for detsik.
hire function k..(t) represems Uzeesdmatedholdup within the indkiduslcomponent
whsn the throughput wss t kilograms.
%roughput      = 10 kg.




                                                                                         101
                           TABLE C-III.      Constnnts ofhstegration’.b

                           ArccI: Glove Box Pksor
                           Measurement Points 3-5

                            Messurnrent          Coordinates (x,y)                  Constants
                                 Point             on ffc4sr (cm)              1           2      3
                                   3              (13.97,42.55)            0.1946     1.670     2.536
                                   4              (54.61, 31.75)           0.3692     7.938     4.670
                                   5              (97.79, 34.29)           0.3692    14.210     4.929
                           %?s fs. 26.
                           %stcctors were reproducibly placed in these locatIOns for sll seven
                           experiments so that the above constmts wsre used in SUcsses.




      TABLE C.IV.      Table of Messurut Holdup Psr Unit Ares”
      Espsrirrrent: U,O,
      Glove Box Floor
                                                                        Tluoughputb
                                                                            (lcslI
                      Measurement
      Airflow            Point               2             4           6               8                  10
                             3            0.0264        0.0902       0.0910         0.1263       0.2020        0.2641
      LOW                    4            0.039s        0.0970       0.1513         0.25S9       0.3094        0.3066
                             s            0.0902        0.1180       0.1646         0.1958       0.3046        0.2682
                             3            0.0211        O.m          0.1941’        0.0609      0.1747         0.1499
      MEDIUM                 4            0.0166        0.0524       0.1955’        0.1211      0.1869         0.1536
                             s            O.0000        0.0744       0.1221         0.1183      0.0s70’        0.1879
                             3            0.1486          ---        0.2285         0.1845       0.1655        0.2768
      HIGH                   4            0.2375        0.2108       0.~72          0.2739       0.2444        0.3280
                             5            0.1920        0.1714       0.2122         0.1135’      0.2995        0.1304’
      ‘The vslues given me scaled to milligrams per qusre cmdmcter, When regressed on the ccmstarrts of integration
      (Table C-III) snd multiplied by c, = 0.3692 times the corresponding throughput (Sec. X33),estimates of the
      psrsmenters (n,~,y) in the denslry fiurctfon sre obts3rsed.Integration of the esdmatcd density yields the essirrmteof
      holdup.
      %cro vstuc.sirrrtkate the observed negative count rate% which may result from measurement error when the smount
      of mstcrhd measured ISsmsll relative to background: blsnks indicate that no vstue is avcilable.
      ‘An outier not used in the model fitting.




      TABLE C-V. Tahle of Messured Holdup Per Unit Arm”
      Expcsinsent: U,O,
      Vcrdcsl Segment
                                                                                                                              I
                                                                        Tbr0u5hput’
                                                                            (k)
                      Mcmurement
      Airnow               Point            2              4           6              8                   10
      LOW                    6            0.0015        0.0039       0.0056         0.0367’     0.0177         0.0282
                             7            0.0082        0.0133       OJX311’        0.0284      0.0220         0.0374
      MEDUM                  6            0.0417        0.oOoo       oJX300         O.0000      0.0470         0.0000
                             7            0.00MI        O.0000       0.0141         0.01S8      0.0538         0.0414
      HIGH                   6            0.0147        0.0420       O.m            0.0028      0.0310         0.0000
                             7            0.0412        0.0837       0.0882         0.0868      0.0646         0.0149
      The v.ches given are scsled to nriUigrsmsper squsre ccrrdnrccer.Wlen regressed on the cmrstsnts of Integration
      (Sec. III), psmnreter estimates in the density function srs obtxined. Integration of the density function yields the
      holdup estimators h(t) as given in Tables C-I srrd C-II.
      bZero vslues indicate the observsd negative count mtcs, which may mmdt from mecsuremerrterror when the smount
      of materisl measured k smsll relative to background; blsnks indicate that no value is wwihble.
      CAnoutlier not used in the mcxfd fitting.




102
     =
     TABLE C-VI.       Tabk of Meceurcd Values
     Experiment: U,O,
     Measurement Points: 8-10, 14
                                                                     lllroughput”
                                                                          h)
                     Meamrcrrrent
     Amow               Point                2        4          6              8                10
     LGW                    8              o.ot37    O.(M3     0.013          0.025     0.034          0.023
     MEDUM                                 O.000     0.000     0.007          0.069     0.096          0.038
     HIGH                                  O.ow      0.044     0.023          0.1s5     0.061          0.122
I
    LOW                     9             0.025      0.031     0.052            –       0.090          0.082
    MEDIUM                                0.032      0.029     0.087          0.153     0.071          0.139
    HI!GH                                 0.069      0.118     0.301          0.261     0.1s9          0.041
    LOW                    10             0.017      0.014     0.010          0.021     0.040          0.041
    MEDIUM                                O.000      0.035     0.040          0.053     0.059          0.049
    HIGH                                  0.023      0.0S6     0.103          0.138     0.077          0.071
    L(3W                  14              0.048      0.117        0.202        0.258        0.373  0.376
    MEDIUM                                0.120      0.247        0.406        0.495        0.687  0.739
    HIGH                                  0.430      0.787        1.090          —          2.316  2.313
    —
    “Zra values indkate ob$ervcd negative count rates, which may result from measurement error when the amount of
    miitericl measured is smell relative to background; blanks indicate that no vclue u qvailable.
    .



    .
    TABLE C-VII.       Table of Mewred Holdup Pcr Unit Length of Duchvork”
    Experiment: U,O,
    Horizontal Segment

                                                                 Throughput”

                     Memmmrent
    AiMow               Point               2         4         6               8                10
    —
                           11            0.0058     0.0074    0.0130         0.0275    0.0275         0.0444
    LC)W                   12            0.0000     0.0000    0.0218         0.0142    0.0418         0.0408
                           13            0.0144     0.0041    0.0174         0.0311    0.0306         0.0471
                           11            0.0000     0.0304    0.0234         0.0543    0.0539         0.0448
    MEDIUM                 12            0.0161     0.0323    0.04ss         0.0645    0.0778         0.0s22
                           13            0.0391     0.0377    0.0555           –-      0.06S6         0.0541
                           11            0.0493     0.0621    0.0798         0.1221’   0.0703         0.03s4’
    HIGH                   12            O.0000     0.0180    0.0740         0.1110    0.0693         0.1129
                           13            0.0334     0.0073    0.0S67         o.tm17    0.0288’        0.0799
    —
    ‘The values given are scald to milligrams pcr qmrc centimeter.
    ?Zcro values ind3cateobserved negative count rates, which may result from mecsuremmt error when the mrount of
    material measured Is smcli relative to background; blanks indicate tbat no vclue is available
    ‘AI) outlier not used in the model fitting.




                                                                                                                    103
      TABLE C. VIII.     Table of Holdup Mcssurscnents”
      Expcdnsent: Cossse U,O,, high xirtlow

                                                              Tbmughpd’


       Measurement
          Point                 2                  4          6               a                 10
              1               O.m            o.ooCa          O.0000        0.0000      0.0000        O.m
              2               0.0000         0.0000          0.0000        0.0000      0.0000        0.0000
              3               0.0000         0.0000          0.0000        O.m         0.02s5        0.0059
              4               0.1031         0.144M          0.1155        0.1225      0.1550        0.1942
              5               0.0277         0.0529          0.0642        0.02s1      0.0374        0.0778
              6               00000          0.0056          O.WKKI        0.0246      0.0290        o.cKmo
              7               0.0006         0.0099          0.0127        0.0325      0.0308        0.0281
              8               OJJ300         0.0120          0.0180        0.0180      0.0180        0.0030’
              9               O.0000         0.00W           O.oow         O.0000      0.0000        0.0000
             10               0.0000         O.m             O.WOO         O.0000      O.m           O.0000
             11               0.0000         OLM300          O.0000        O.m         O.ooml        O.0000
             12               0.0000         0.0000          0.0199        0.0209      0.0066        0.0000
             13               0.0000         0.0041          0.0114        0.0000      0.0000        OJMOO
             14               0.1630         0.18643         0.2740        0.3520      0.4480        0.4270

      ‘At each measurement point, tabukcte vshces sre scslcd cs In the experiments with U,O, (set Tablss C-IV through
                                                u uc
      C. VII); that Is, for locations 1.7 md11-13 ccits cssilligmsssspersqusue csnthnstcr, msdfor locations 8.10 md14
      units me grsms.
                 indicate obsawsd negative mum rates, wtdch may ccsult from measurement error when the snsount of
      “Zero VSIUCS
      matmisl messurcd is smsll relstlve to background; blsnks indicate that no vahceis malhible.
      ‘An outlier not used in she model titrhsg.




                     Table C-IX. Summsry of Modeling Results for Expxciment with
                                 Cocrse UjO,

                                           Mecsummcnt                                 Estirnnted Holdupc
                     Comoonent               Points’                  Model                    (Is)
                     Glove box sides                   I-2           6,(t) = o                  0
                     Glove box floor                   3-5        Ii#) = o.0934t            0.934
                     Vertical segment                  6-7        IiJt) = o.0199t           0.199
                     First elhow                        8         fi,(t) = O.oozzt          0.022
                     Segment Lsetwccn
                      elbows                            9            ~(t) =0                    o
                     Second elbow                      10            Ii,(t) = o                 0
                     Horizontal
                      segment                      11-13             fih(t) = o                 0
                     Filter                            14         ~t) = 0.1241
                                                                      + 0.0118t             0.440
                                                                      + o.oo20t~
                     System totcl                  1-14            fi(t) = 0.1241           1.595
                                                                         + 0.1273(
                                                                         + o.oo20t*
                     System weight
                       10ss                                                                 2.266
                     ‘.% Fig. 6 for detsils.
                     %C function fi...(t) rsprsscnts the estimated holdup within the individual
                     mmponcnt when the throughput was t kilogrccns.
                     Throughput = 10 kg.




104
I
    TABLE C-X.      Table of Holduo Measurements*
    Espsriment: Ash, low sirflow
                                                    Tlu’ougbputb
                                                            fks)
     Measurement
         Point              1          2              3                 4              s            7            10
           1           o.oa30       O.omo             -.              O.woo         O.0000 O.ocm               0.0000
           2           O.moo        o.cmcKl           ...             O.0000        O.oow O.cow                0.0000
           3           0.0262       0.0352       0.0494               0.0611        0.0625        0.1133       0.1389
           4            -.      —.                 —                    —             .-            —            —
           5           0.0109 0.0180             0.0310               0.0312           —          0.0535       0.0874
           6           0.0101       0.0079         —                    .-             —            -.         0.0149
           7           0.0076       0.0062         —                    —              —           -.   0.0096
           8           0.0040       0.0010       0.0070               0.0020 0.0080               0.0080 -.
           9           0.W40        0.0000         -.                   —       —                  -.   0.016J3
           10          O.m          0.0000       0.0000               0.CH330 0.0050 0.00250 0.0060
           11          O.0000       0.ooOO         ...                  —       .-      —.   Omoo
           12          O.lnoo       O.w          0.ooOO               O.mcso  0.ooOO O.0000 OSKJOO
           13          O.ocm        O.0000         ...                          —       -.   O.0000
           14          0.0330       0.0360       0.0360               0.0470 o.06c0 0.0564J 0.1030
    “At each measurement point, tabulated vslues cm scslcd cc in the experiments with U,O, (see Tables C-IV through
    C-VII); tbat 1s,for locations I-7 cnd 11-13 units me ndlligmrns per squszs caxtinretcr, and for locations 8-IO snd 14
    units szc 8rc2s2s.
    %ro values indicate the observed negative count rates, wtdch may red from measurement ecror when the smount
    of materiel measured k smstl relative to background; blsccks ind”catc no VCIUC avcilablc.
                                                                       that       k




                      C-XLSummscy Modeling
                   Table        of                                   Results for Low-Airflow Experiment
                                   with Ash                                                 .

                                           Mcssurcmcnt                                     Estimated Holdupc
                   Comrsonent                Points’                    Modclb                      (R)
                   GIove Lwx sides             1-2                      =o
                                                                     6,(t)                         o
                   Glove box flmr              3-5                    =0.1436t
                                                                   fi#)                          1.436
                   Verticsl segment            6-7                    =o.(M94t
                                                                   &(t)                          0.094
                   First elbow                  8                     =o.oo13t
                                                                   fil(t)                        0.013
                   Segment bstween
                     eIbows                     9                     = 0.0016t
                                                                   fib(t)                        0.016
                        elbow
                   Second                       10                 fiz(t) = 0.00056t             0.0056
                   Horizontsd
                     segment                  11-13                    fi,(t) = O                  o
                   Filter                       14                  ~t) = 0.0329                 0.100
                                                                        + o.t30433t
                                                                        + o.0006t2

                   System total                1-14                 fi(t) = 0.0329               1.664
                                                                          + 0.1568t
                                                                          + o.0006t2
                   System weight
                     loss                                                                         1.31
                   %ce Fig. 6 for dctcils.
                   %C function ft...(t) represents thccstirnzdcd holdup within the individual component
                   wben the throughput was t Id!qrcms.
                   Throughput = 10 kg.




                                                                                                                            105
      TABLE C-XII.     Table of Holdup Measurements”
      Experiment: Ash, medium aidlow
                                                                         Throughputb



           Point          1        2         3          4          5         6            7        8          9             10
              1        O.oocm        os30000.0000 0.0000 0.0000 0.0000 O.m      0.0000 O.wxl 0.0000                              0.0000
              2        0.00WI 0.0000 o.ooca30.0000 O.omo 0.0000 O.0000 0.0000 0.0000 O.0000 ooooo                                O.oocm
              3        0.0081 0.0071 0.0143 0.0138 0.0344 0.0264 -.     0.0259 0.0420 0.0640 0.0501                              0.0542
              4        oSlooo        0.0175 0.0330 0.04140.0592 0.0S10 0.0626 0.0671 0.0916 0.0879                                 —.
              5        0.0073 0.ooOO 0.0197 0.0228 0.04400.0324 0.0420 0.0541 0.0479 0.0696 0.0671                                 ...
              6        OSX347 0.0003 0.0000 0.0000 0.0000O.ocm O.cmo O.0000O.owa 0.00W 0.0034                                    0.0000
              7          — 0.(K393   0.0181 0.0113 0.0164 0.0161 0.01270.0065 0.0088 0.IJ382 0.0099                              0.0150
              8        0.0140 00010 0.00s0 O.mo 0.0000 0.0070 0.0060 0.0340 0.0260 0.0260 0.0280                                 0.0290
              9        0.0280 0.0290 0.0210 0.0330 —        .— 0.04200.0400 0.0550 0.0430 0.0290                                 0.0570
             10        0.0110 0.0080 0.0090 0.0140 0.0060 0.0110 0.0200 0.0210 —       0.0240 0.0220                             0.0260
             11        0.0119 0.0074 0.0119 0.0058 0.0127 0.0140 0.0201 0.0119 0.0132 0.0132 0.0160                              0.0148
             12        0.W19 0.0066 0.0133 0.0085 0.0085 o.m57 0.0171 0.0114 0.0161 0.0190 0.0209                                0.0285
             13        0.0046 0.0082 OJXM9  0.0087 0.0187 0.0050 0.0119 0.0087 0.0069 0.0128 0.0091                              0.0164
             14        0.0540 0.0750 0.1130 0.1370 0.15700.1880 -.      0.1440’ 0.2770 0.3200 0.2830                             0.2730
                           p
      “Ate-cb measurement olnt,tabuistcdvstucsuc !estsd u in thecxpcrimcms withU,O (sesTablesC.lV throughC.VII);IM k forImations 1.7and
                             pa
      11.13unitsarc milligrams squarecatimetsr, and for loc.tions 8.1o and 14tudts L c grsms.
      %%o vahm indicatethe observednegativemunt rates, whichmay rcsuh from mcasurememerror whenthe amountof mata”sl measuredis small
      mlmivcto background;blanksindiate that no valueis avmilable.
      ‘Anoutlkr not usedin the mcdd II@.




                                                                                              —
                              Table C-XIII.      Summary of Modeling Results for Mutiurn-Airflow                  Experi-
                                                 ment with Ash
                                                       Measurement                                Estimated Holdupc
                              Component                  Points’                 Modelb                  (i4)
                              Glove box sides               1-2              fi,(t) =   o                0
                              Glove box floor               3-5        ~t)       = 0.0676t             0.676
                              Vertical segment              6-7        &(t) = oO045t                   0.045
                              First eltmw                    8         fi,(t) = o.oo25t                0.025
                              Segment between                9         fib(t) = 0.0227                 0.046
                                elbows                                       + o.oo23t
                              Second elbow                  10            =0.0024
                                                                       fil(t)                          0.024
                              Horizontal
                               segment                               =o.oo90t
                                                            11-13 lih(t)                               0090
                              Filter                         14      =0.0273
                                                                  fi~t)                                0.295
                                                                     + 0.0267t
                              System total                  1-14       Ii(t) = 0.0500                  1.201
                                                                             + 0.115 It
                              System weight
                                loss                                                                   1.53
                              %e Fig. 6 for dstails.
                              %e function 6...(t) rsprssents rlzeesdnmwdholdup within theindlvidual componmt
                              when the throughput was tkitogmms.
                              Throughput = IO k8.




106
TABLEC-XIV. Table of    fiddw       Msssuransnts’
Espmmsm: Ads, MgbSisnow
                                                                              Tbrm@pln’
  Msssurancnl
     Point          1           2       3          4           5          6            7     8           9             10
        1        0.0000 0.oOoo O.omo            O.omo               Oaoo          O.oom    0.oOoo    oJ3000 0.oOoo omooo O.omo
        2        0.oOoo O.omo O.oom             o.oOoo       0.0000omooo          O.moo    O.oom     O.omo  Oomo o.oOoo O.omo
        3        O.omo 0.0383 o.02511           0.0276       0.0724 0.0s30        0.0893   0.0684    0.1118 0.1096 0.1088 0.1074
        4        0.W82 0.0434 0.0786            0.07s0       0.1127 0.0992        O.lom    0.1074    0.1618 0.1451 0.1443 0.1471
        5        0.0265 0.0065 0.0569           0.0775       0.0789 0.1026        0.1110   0.1274    0.1457 0.1764 0.1637 0.1460
        6        O.oom 0.0095 0.W95             0.0040       0.W78    -.            —      0.0243    0.0214 0.0211 0.01s7 —
        7        0.0178 0.0189 —                0.0291       0.0319 0.0332        0.0322   0.0281             -.   0.0456 0.M45
        8        0.0160 0.0340 0.0240           0.0320       0.0140 0.0164        0.0330   0.0360    O.MLW 0.03s0 0.0280 0.0320
        9        0.0230 O.oom 0.oOoo            o.03m               O.mm          0.0350   O.osw     0.0230 o.m70 O.mm 0.0290
       10        0.0000 0.0040 O.omo            o.mso        0.0030 o.m20         0.0110   0.0110    o.m30 o.m20    —     o.olm
       11        0.0064 0.00ss O.moo            0.0164       O.moo 0.W66          0.oOoo   0.0132    O.moo O.omo o.oOoo O.oom
       12        0.0000 0.0047 o.m28            0.0228       0.0114 o.m38         0.0171   O.oom     Oaooo 0.W38     o.m57 0.0161
       13        o.m73 0.0123 O.moo             0.0174       0.0132 0.01ss        0.0187   0.0279    O.0000 0.0069   0.0160 0.W64
       14        0.0750 0.14W 0.1870            0.2630       0.3030 0.4280        0.47s0             0.6180 0.7230   0.739U 0.6660
‘At sach measurement point,mbulated vatucs are scatsd q in tie experiments with U, 0, (scs Tables C-IV tbrougb C-VII); that is for
                                            p
locations 1-7 and 11-13 writs sre rrdlUgrmsrs sr squsre cendmctsr, and for lodons 8-10 and 14 units are grmsss.
bZrro values indicate the obscrvrd negative mum rstss, wldch may rewlt from messursment error when tbe smount of nsaterisl
                                                                      is
messured is small relative to background; blanks indicate that no VX3UC avsihble.




                        Table C-XV.         Sorrrsnssy of Modeling Results for High-Airflow              Expcsinrent
                                            with
                                               Ash
                                                Measurement                                Estimated     HoldupC
                        Component                 Points”                     Modelb                  (B)
                        Glove box sides                 1-2               fi,(t) = o                 0
                        Glove box floor                3-5          ~t)       = 0.1466t             1.466
                        Verticsl segment               6-7          &(t) = o.0207t               0.207
                        First dbOW                      8           6,(t) = 0.0197               0.035
                                                                              +   O.oolst
                        Segment between
                         elbows                         9           &(t) = o.fKt24t              0.024
                        Second elbow                    10          fii(t) = 0.0008t             0.008
                        Horizontal
                         segment                       11-13        fi,(t) = 0.~56t              0.056
                        Filter                          14          $.(t) = 0.0622               0.707
                                                                         + 0.0008tz
                        System total                   1-14          6(t) = 0.0197                  2.503
                                                                          + 0.2398t
                                                                          + 0.0008t]
                        System weight
                          loss                                                                   3.06
                        ‘See Fig. 6 for dstsits.

                        when the throughput &as t kilogrsmss.
                        Throughput = IO kg.




                                                                                                                                     107
      DATA FROM EXPERIMENTAL STUDY OF
      URANIUM HOLDUP IN A LIQUID-LIQUID
         EXTRACTION PULSE COLUMN
            (Tables C-XVI and C-XVII)




108
.




    Table
       C-XVI. Concentration Rofde Data
                                            Experimental Run 2A-3
            ExtractiotiScrub    COhSMSS   (I-A)                   stiDssillsI   COhSMSS   (1-B)
                      Aqueous Orgsmic                                          Aqueous Organic
    Sample’ Imcationb Ursniumc Ur.snhsmc                     Samole’ Locationb Uraniumc Uraniumc
    A-1              0.s       0.106         5.208          B-1           0.5       1.487         0.561
    A-2             12.5       0.406         5.705          B-2          18.5       2.568         0.723
    A-3             24.5       0.749         6.436          B-3          36.5       3.827         1.014
    AA              36.5       0.950         6.790          B4           54.5       5.731         1.353
    A-5             48.5       0.965         6.888          B-5          72.5       6.732         1.561
    A-6             52.5       1.281         6.337          B-6          90.5       8.021         1.854
    A-7             64.5       0.736         5.598          B-7         104.5       8.805         2.011
    A-8             76.5       0.251         2.767
    A-9             88.s       0.110         0.840
    A-IO           105.5       0.066         0.287
    A-11           129.S       0.047         0.045
       Flu.
    ‘SCS 20.
    he     top of the working saction cormqmnds to the vslue zero, and each stage has unit len@ls.
    ~e     values given are in units of grams of urasdudsrsge.




    Table C-XVII.       Concentration Rofie Data
                                       ExocrisnentalRun 2D-2
           Extractiorr/Scrub COhMSIS (1-A)                           Column (1-B)
                                                             StSiDDisM
                      Aqueous &@SliC                                          Aqueous Organic
    Sample’ Locationb Urarsiumc Uraniumc                    Sample’ LOcationb UraniumC Ursmiumc
    A-1             0.5        0.213 7.841                 B-1           0.5        0.063         0.005
    A-2            12.5        1.057        8.52S          B-2          18.5        0.084         0.006
    A-3            24.5        1.512        9.131          B-3          36.5        0.397         0.016
    A-4            36.5        1.743        9.570          B4           54.5        5.089         0.474
    A-5            48.5        1.864        9.825          B-5          72.5        9.551         1.145
    A-6            52.5        2.354        9.412          B-6          90.5       13.554         1.709
    A-7            64.5        2.323        9.328          B-7         104.5       15.253         1.953
    A-8            76.3        2.057        8.849
    A-9            88.5        1.002        6.233
    A-10          105.5        0.059        0.899
    A-11          129.5        0.008        0.059
    %eeFig. 20,
    %e topof the workingsectioncorreqmndsto the value zero, and aachstagehas urdtkngth.
    The valuesgivenare in urdtsof grams of Uranium/stage.




                                                                                                          109
      DATA FROM EXPERIMENTAL STUDY OF URANIUM HOLDUP
         DURING ADU PRECIPITATION AND CALCINATION
                  (TablesC-XVIII through C-XXII)




110
   C-XVIII. of
Table               irr
                     the      Column
         HoldupUranium Precipitation
 Throughput        Holdup           Error             Throughput     Holdup     Error
       U)
  (kg of            of
                   (g u)           of
                                  (g u)”                 o U)
                                                       (kgf           of
                                                                     (g u)      of
                                                                               (g u)”
      1            4.66           0.11             29                 72.30     0.50
     2           27.13            0.23             30                 20.25      0.30
     3             7.17           0.15             31                 14.60      0.30
     4           45.56            0.31                                12.60      0.30
     5            12,90           0.21       IClemflut #l]             —          —
     6             7.93           0.17             33                  8.23      0.25
     7             7,00           0.16             34                  6.82      0.23
     8            10.23           0.20             35                  8.12      0.26
     9           33.29            0.29             36                  9.82      0.23
    10            17.84           0.27             37                  7.63      0.25
    11           22.07            0.28             38                  7.98      0.26
    12           23.28            0.32             39                  8.25      0.27
    13           28.17            0.35                                 8,82      0.27
    14           64.63            0.46       IClemVut #2]              —          -.
    15           48.52            0.47            41                  55.57      0,57
    16           50.23            0.48            42                  55.25      0.58
    17           78.67            0.51            43                  17.48      0.39
    18           52.25            0.51            44                   5.22      0.21
    19           67.78            0.55            45                  10.95      0.26
    20           52.29            0.50            46                  10.45      0.29
    21           58.02            0.48            47                   6.87      0.25
    22           46.28            0.46            48                   7.72      0.26
    23           42.89            0.46            49                   8.02      0.18
    24           46.39            0.47             50                  9.65      0.20
    25           31.90            0.46            51                   8,87      0.21
    26           33.60            0.34                                 9.27      0.20
    27           22.28            0.33       IClear?vut#3]             .-         —
    2a           10.81            0.2s
%e errors
        reported here are counting errors ordy.




Table C-XIX.    Holdup of Uranium in the Filter Funnels
  nlrougbput       Holdup                             -llu’oUgbput    Holdup
   (kg of u)       (g of u)       (%)’                 (kg of u)     (gOfu)    (s%)”
        1             2.32           0.01                 27          10.40      O.w
        2             4.32           0.02                 28           4.36      0.03
       3              6.01           0.02                 29           9.74      0.04
       4              7.13           0.02                 30           7.22      0.04
       5             13.32           0.04                 31          12.15      0.03
       6             12.03           0.03                 32           5.92      0.05
       7             16.11           0.04                 33           8.99      0.05
       8             13.80           0.04                 34           7.13      0.06
       9             16.54           0.04                 3s           8.01      0.0s
      10             15.02           0.04                 36           8.84      0.05
      11             11.74           0.04                 37          11.18      0.05
      12             12.31           0.04                 38           6.47      0.04
      13             10.06           0.04                 39           7.46      0.0s
      14              9.23           0.03                 40           5.26      0.04
      15             10.24           0.04                 41           9.99      0.06
      16             10.21           0.04                 42           8.24      0.0s
      17             10.91           0.04                 43           9.54      0.05
      18             13.48           0.04                 44           5.87      0.05
      19             12.40           0.04                 4s           7.29      0.0s
      20             11.49           0.04                 46           6.45      0.0s
      21             11.06           0.03                 47           9.22      0.06
      22              8.92           OJM                  48           9.56      0.06
      23              9.99           0.04                 49           8.36      0.04
      24             11.34           0.04                 50           6.48      0.04
      25              7.22           0.04                 51           8.89      0.04
      26             10.33           0.04                 52          10.11      0.04
‘TIMerrors reported here are counting a’rors   odY.


                                                                                        111
      Table C-XX.       Holdup of Uranium in the Calciner
       Throughput          Holdup           Error       TbrOugbput   Holdup       Error
        (k8 of u)          (g of u)       (g of   u)’    (kg u)
                                                            of       (g Ofu)    (g of u)”
                1            0.07           0.01            27         1.17       0.01
               2             0.30           0.01            28         1.11       0.01
               3             0.64           0.01            29         1.17       0.02
               4             0.67           0.01            30         1.16       0.02
               s             0.66           0.01            31         1.20       0.02
               6             0.87           0.01            32         1.2s       0.02
               7             1.00           0.01            33         1.11       0.02
               8             1.12           0.01            34         1.14       0.02
               9             1.21           0.01            3s         1.16       0.02
              10             1.19           0.01            36         1.18       0.02
              11             1.19           0.01            37         1.18       0.02
              12             1.20           0.01            38         1.16       0.02
              13             1.15           0.01            39         1.18       0.02
              14             1.18           0.01            40         1.15       0.02
              15             1.30           0.01            41         1.38       0.02
              16             1.24           0.01            42         1.31       0.02
              17             1.23           0.01            43         1.26       0.02
              18             1.21           0.01            44         1.34       0.02
              19             1.20           0.01            45         1.41       0.02
              20             1.18           0.01            46         1.76       0.03
              21             1.18           0.01            47         1.48       0.02
              22             1.20           0.01            48         1.33       0.03
              23             1.23           0.01            49         1.56       0.02
              24             1.21           0.01            so         1.6S       0.02
              2s             1.20           0.02            51         1.74       0.02
              26             1.19           0.02            52         1.74       0.02
      ~e     errors mmrted here are couminR irrors only,




      Table C-XXI. Holdup of Urmdum in tbe CaMrrcr Trays
           Throughput        Holdup         Error       Tbrm@put     Holdup
            (kg of u)       (g of u)      (g of u)”      (kg of u)   (g of u)   (ET;)”
                1            0.11            0.01           27         0.80       0.01
                2            0.17            0.01           28         0.82       0.01
                3            0.20            0.01           29         0.96       0.02
                4            0.28            0.01           30         0.92       0.02
                5            0.30            0.01           31         0.98       0.02
                6            0.29            0.01           32         1.01       0.02
                7            0.30            0.01           33         0.95       0.02
                8            0.32            0.01           34         1.03       0.02
                9            0.35            0.01           35         1.00       0.02
               10            0.40            0.01           36         1.04       0.02
               11            0.41            0.01           37         0.94       0.02
               12            0.41            0.01           38         1.01       0.02
               13            0.38            0.01           39         1.02       0.02
               14            0.43            0.01           40         1.04       0.02
               15            0.41            0.01           41         1.17       0.02
               16            0.44            0.01           42         1.11       0.02
               17            0.45            0.01           43         1.12       0.03
               18            0.53            0.01           44         1.25       0.03
               19            0.66            0.02           45         1.09       0.03
               20            0.57            0.01           46         1.08       0.03
               21            0.56            0.01           47         1.14       0.03
               22            0.60            0.01           48         1.58       0.03
               23            0.56            0.01           49         1.30       0.02
               24            0.64            0.01           50         1.46       0.02
               25            0.68            0.01           51         1.43       0.02
               26            0.77            0.01           52         1.35       0.02
      %e errors rermrred here are counting errors ordy.




112
    Table C-XXII.     Holdup of Uranium in the Dissolver Vessel
      Throughput Holdup                               TluOughput   HOkiUP       Emor

       (kg   of u)      (g of u)       J%;)”           (kg of U)   (g of u)   (g of u)’
I             1          0.31             0.01            27        0.71        0.01
              2          0.66             0.01            28        0.80        0.01
              3           1.32            0.01            29        0.96        0.01
              4          0.92             0.01            30        0.58        0.01
              s          0.81             0.01            31        1.13        0.02
              6          0.84             0.01            32        0.80        0.01
              7          1.62             0.01            33        0.77        0.02
              8          0.88             0.01            34        0.80        0.02
              9          0.92             0.01            3s .      0.65        0.02
             10          0.73             0.01            36        0.62        0.02
             11          0.96             0.01            37        0.74        0.02
             12          0.61             0.01            38        0.7s        0.02
             13          0.86             0.01            39        0.77        0.02
             14          0.85             0.01            40        0.86        0.02
             15          0.58             0.01            41        0.70        0.02
             16          0.58             0.01            42        0.71        0.02
             17          1.54             0.02            43        0.56        0.02
             18          0.74             0.01            44        0.70        0.02
             19          0.70             0.01            45        0.74        0.02
             20          0.71             0.01            46        0.68        0.02
             21          0.74             0.01            47        1.03        0.02
             22          0.62             0.01            48        0.98        0.02
             23          0.60             0.01            49        0.98        0.02
             24          0.88             0.01            50        0.90        0.02
             25          1.36             0.02            51        0.64        0.02
             26          0.84             0.01            52        0.73        0.02
    “The errors reporred here are counting errors only.




                                                                                          113
      DATA FROM EXPERIMENTAL STUDY OF
      URANIUM HOLDUP IN SOLUTION LOOPS
         (TablesC-XXIII through C-XXVII)




114
TABLE C. XXIII.                         E.xouimcnts: CPVC Lam. Low Flow Rate
                  Data &om Solution LZJOD

                                                   Locationa
   Thrcugbput      101     102     io3               10s        106    107     10B    109
    (Mg   U)       (d      (s)     (8)     (%         (g)      (g/m)   (g)    (g/m)   (g)
      0.018        0.98   0.01    0.02     0.05      0.01      0.02    0.01   0.01    0.00
      1.295        9.70   0.16    0.69     0.5s      0.20      0.15    0.12   0.08    0.14
      4,106       1s.37   0.18    0.68     0.47      0.16      0.11    0.10   0.06    0.13
      9.889       24.19   0.18    0.3s     0.46      0.15      0.13    0.10   0.09    0.16
     14.262       24.89   0.09    0.30     0.49      0.13      0.09    0.11   0.06    0.17
     20.lIM       26.78   0.2s    0.4      0.47      0.13      0.10    0.13   0.1s    0.16
     24.422       31.89   0.25    0.55     0.ss      0.12      0.17    0.12   0.14    0.12
     28.920       37.91   0.26    0.31     0.51      0.18      0.13    0.13   0.06    0.11
     34.1s4       38.29   0.23    0.29     0.48      0.11      0.15    0.11   0.15    0.11
     40.129       40.18   0.27    0.46     0.50      0.22      0.15    0.15   0.13    0.11
     42.490.      34.51   0.30    0.31     0.27      0.11      0.08    0.12   0.15    0.12
                                                   LOtxtion’
  Throughput       110     111     112     113       114       115     116    117
    (Mg u)         (a)     (8)     (S)    (g/m)       (g)       (8)     (s)    (8)
      0.018       O.w     0.01    0.01     0.02      0.00      0.01    0.01   0.00
     1.29S        0.09    0.25    0.29     0.s3      0.22      0.69    0.23   0.66
     4.106        0.09    0.24    0.30     0.68      0.21      0.77    0.25   0.65
     9.889        0.09    0.19    0.26     0.70      0.19      0.58    0.25   0.s0
    14,262        0.09    0.16    0.29     0.69      0.19      0.42    0.24   0.78
    20.104        0.10    0.16    0.30     0.71      0.19      O.u     0.23   0.78
    24.422        0.11    0.15    0.28     0.72      0.19      0.63    0.23   0.67
    28.920        0.11    0.13    0.23     0.65      0.20      0.45    0.24   0.s4
    34.1s4        0.10    0.37    0.27     0.41      0.18      0.41    0.30   0.70
    40.129        0.22    0.15    0.26     0.86      0.20      0.58    0.23   0.62
    42.490        0.11    0.16    0.22     0.69      0.17      0.55    0.20   0.78
‘SeeFk.47.




TABLEC-XX3V. Dm !?om Solution tip        Exp&ntcnts:CPVCLoop,H@ FlowRate

                                                   Lncat50n’
  Throughput       101     102     103      104      105       106      107    108     109
    (tvIgu)        (8)     (g)     (s)     (g/m)     (g)       Wm)      (g)   (g/m)    (8)
     42.610        8.s6   0.10    0.24     0.36      0.12      0.10    0.09   0.04    0.11
     47.436       10.54   0.08    0.29     0.34      0.12      0.13    0.06   0.09    0.08
     S9.568       13.41   0.10    0.48     0.34      0.10      0.07    0.07   0.09    0.08
     68.354       17.36   0.11    0.48     0.31      0.10      0.09    0.05   0.09    0.06
     79.886       10.50   0.07    0.14     0.38      0.1 I     0.11    0.08   0.03    0.08
     88.567       11.52   0.12    0.67     0.39      0.11      0.13    0.09   0.07    0.09
     91.5s5       10.92   0.06    0.10     0.42      0.12      0.14    0.04   0.06    0.06
                                                   Laation’
  Throughput       110     111     112     113       114        115     116    117
    (Mg u)         63)     (s)     (c)     @m)        (g)       (g)     (g)    (g)
    42.610        0.08    0.13    0.19     0.64      0.15      0.40    0.21   0.60
    47.436        0.0s    0.13    0.19     0.2s      0.14      0.47    0.07   0.63
    59.568        0.06    0.11    0.20     0.48      0.14      0.51    0.20   0.62
    68.354        0.04    0.13    0.22     0.63      0.18      0.93    0.18   0.73
    79.886        0.06    0.13    0.22     0.54      0.16      0.81    0.18   0.90
    88.567        0.08    0.13    0.20     0.83      0.22      0.99    0.20   0.93
    91.555        0.0s    0.13    0.18     0.52      0.17      0.33    0.17   0.87
% Fia. 47.




                                                                                             115
      TABLEC-XXV. Dms                         SMhIest LOOP.LOWHOWRate
                     horn Solution LOOPExpcrimmtb’: steel

                                                         Location’
          Throughput               2       3
            Wtl w        (:)      (8)     (8)   ~’m)         ;)       ~6m)     ~)      W8m)    (;)
             0.073       1.63     0.40   0.58   0.16        0.54      2.3s     0.08    0.12    0.06
             2.321       4.00     0.28   1.19   0.28        0.43      131      0.10    0.15    0.06
             5.764       7.90     0.28   0.65   0.04        0.45      1.41     0.09    0.11    0.07
             9.343       8.52     0.23   0.87   0.60        0.44      1.55     0.06    0.01    0.10
            14.6S1       7.73     0.22   0.s8   0.14        0.44      1.56     0.07    0.10    0.12
            18.633      10.32     0.26   0.67   0.13        0.44      1.73     0.09    0.31    0.14
            2A.049      10.20     0.19   0.70   0.23        0.46      1.63     0.11    0.18    0.14
            27.646       7.81     0.21   1.34   0.26        0.44      1.58     0.09    0.14    0.12
            32.417       7.21     0.16   0.63   0.21        0.46      1.66     0.10    0.20    0.13
            36.441       8.10     0.23   0.77   0.03        0.44      1.s5     0.10    0.16    0.13
            41.187      12.57     0.17   0.67   0.13        0.47      1.72     0.08    0.13    0.11
                                                         Lodon’
          -nlrOughput                     12
            (Mg U)       :        ;8’I    (E)   ;:)          ;         ;:;:;
             0.073      0.05      0.04   0.04   0.17        0.03      0.10     0.07    0.25
             2.321      0.08      0.14   0.06   0.12        0.02      0.17     0.04    0.15
             5.764      0.06      0.07   0.11   0.21        0.03      0.09     0.08    0.27
             9.343      0.05      0.06   0.08   0.28        0.05      0.36     0.06    0.20
            14.651      0.08      0.07   0.09   0.37        0.06      0.37     0.06    0.21
            18.633      0.09      0.07   0.09   0.30        0.0s      0.40     0.05    0.20
            24.049      0.10      0.08   0.09   0.30        0.04      0.37     0.06    0.25
            27.646      0.09      0.05   0.07   0.26        0.04      0.36     0.07    0.27
            32.417      0.10      0.07   0.09   0.23        0.04      0.38     0.06    0.24
            36.441      0.10      0.06   0.08   0.26        0.04      0.38     0.06    0.30
            41.187      0.09      0.05   0.08   0.24        0.04      0.37     0.06    0.31
      %.x F&. 46.




      TASLEC-XXVI. DIUS Solution LoopExpcrlmmts: tainless
                      from                     S        SteelLoop,HJgbFlowRate

                                                          Location’

          Throughput
             wiI ~           :)    i)      i)    w:)             :)   W6m)      (:)    W8m)     (j
              41.237     7.53     0.27   0.44    0.07        0.43      1.49     0.04   0.12     0.08
              46.942     953      0.21   0.89    0.16        0.49      1.72     0.10   0.19     0.13
              S9.881     8.74     0.19   1.01    0.15        0.49      1.67     0.08   0.09     0.11
              68.971     7,14     0.23   1.04    0.11        0.47      1.72     0.09   0.12     0.16
              81.312     8.27     0.21   0.%     0.18        0.51      2.88     0.09   0.14     0.17
              90.029    10.18     0.11   0.72    0.0s        0.51      1.83     0.10   0.17     0.18
             100.673     9.21     0.16   0.78    0.03        0.53      1.80     0.11   0.16     0.16
                                                       L0mt50n’
           Throughput                                                            16
            (Mg U)           :     k:      ::    J:)             ;      :        (s)     :;
              41.237     0.07     0.05   0.07    0.26        0.03      0.15     0.06    0.27
              46.942     0.10     0.05   0.06    0.20        0.03      0.25     0.07    0.29
              59.881     0.08     0.05   0.07    0.27        0.04      0.31     0.07    0.30
              68.971     0.09     0.07   0.06    0.22        0.03      0.46     0.11    0.38
              81312      0.10     0.06   0.08    0.30        0.05      0.s0     0.12    0.43
              90.029     0.11     0.08   0.08    0.23        0.05      0.41     0.15    0.62
             100.673     0.09     0.08   0.12    0.50        0.09      0.38     0.14    0.52
      =    F& 46.




116
I
I




    Table C-XXVII.             E       forEsch
                          Holdup sthmtes*           Lomtionstthe
                                              Mmmmmnt
                                  o
                          Cmchuionf theExpcrirncnt
                          LowFlowItatt                   HI@ F30w
                                                                Rote

    Lac.adonb        SS      CPVC     13itTcrcnce   SS         CPVC DifYercncc
     2/102         0.17       0.30      -0.13       0.16       0.06     0.10
     3/103         0.67       0.31       0.36       0.78       0.17     0.61
     4/104         0.12       0.32      -0.20       0.04       0.41    -0.37
     5/105         0.47       0.12       0.36       0.53       0.12     0.39
     6/106         1.69       0.09       1.60       1.81       0.14     1.67
     7/107         0.08       0.12      -0.04       0.11       0.04     0.07
     Ivlos         0.14       0.15      -0.01       0.16       0.06     0.10
     9/109         0.11       0.12      -0.01       0.16       0.06     0.10
    10/110         0.09       0.12      -0.03       0.09       0.05     O.M
    11/111         0.05       0.16      -0.11       0.08       0.13    -0.05
    12/112         0.08       0.23      -0.15       0.12       0.18    -0.06
    13/113         0.24       0.71      -0.47       0.46       0.56    4.10
    14/114         0.04       0.17      -0.13       0.09       0.17    -0.08
    1s/11s         0.37       0.55      -O.ls       0.38       0.34     0.04
    16/116         0.06       0.20      -0.14       0.14       0.17    -0.03
    17/117         0.31       0.77      -0.46       0.52       0.87    4.3s
    “Unitsam io grurra of uranium CXCCIX Urc pipes, Acre holdup is expressed in
                                       for
    grams ofurwdum p      mew dpip,   u iudicucd io F@. 49-W
    %c F&s. 46 urd 47.




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118
IRC FORM         ~                                                                           U S NuCLEAR   REGuLATORY       COMMISSION      1 REPORT       NuMBER     /AsI,smd     b“ TIOC. qdd Vol No    tt ,nvl
;83)
                                                                                                                                                       NUREG/CR-3678
                                           BIBLIOGRAPHIC DATA SHEET                                                                                    LA-1OO38

                                                                                                                                            2    Lmw   b!ank

    TITLE   A?.10    SUET$TLE                                                                                                               4    RECIPIENTS       ACCESSION    NUMEER


        Estimation Methods for Process Holdup
                                                                                                                                            5 DATE       REPORT    COMPLETEO
        of Special Nuclear Materials
                                                                                                                                                 MONTH                               YEAR


                                                                                                                                                February                                 1984
    AuT140RISI                                                                                                                              7 OATE       REPORT    ISSUEO

                                                                                                                                                 MONTH                               YEAR
C.     K. S. Pillay, R. R. Picard, R. S. Marshall
                                                                                                                                                June                                        1984
                                                                                                                                            9 PROJECT/TASK/WORK             UNIT     NuMBER

    PERFORMING        ORGANIZATION         NAME   ANO MAILING   ADDREss   O.dtide       Z,O C.dd

Los Alamos National Laboratory
:OS Alamos, NM 87545                                                                                                                        10    FIN NUMBER




                                                                                                                                                A7226
I sPONSORING ORGANIZATION NAME AND MAILING ADDRESS                           IIncktd.   Z,P cod,)                                           12a TYPE OF REPORT

Mvi.sion of Facility Operations                                                                                                                 Formal
)ffice of Nuclear Research
J. S. Nuclear Regulatory Commission                                                                                                         12b PERIOO         COVEREO   //nc/uIIm    d~tcr)

Washington, DC 20555
3 SUPPLEMENTARY              NOTES




4 ABSTRACT           (2W   wodr   or led


    Los Alamos National Laboratory studied the use of statistical estimation methods for
~terials holdup at highly enriched uranium (HEU)-processing facilities.  Use of historical
~oldup data from processing    facilities    and selected holdup measurements at two operating
;acilities  confirm the need for high–quality        data and reasonable        control over process
~arameters in develop J.ng these models.       Large-scale    experiments were conducted to demon-
strate the value of the models from good-quality           experimental     data.    Using these data,
re developed statistical   models to estimate residual          inventories     of uranium in large
~rocess equipment and facilities.         Some important findings are the following:

J Holdup in some equipment at HEu-processirig facilities,        such as air filters,     ductwork,
  Calciners,    dissolvers,    pumps, pipes, and pipefittings  can be readily modeled.
I Holdup profiles      of process equipment such as glove boxes, precipitators,       and rotary drum
  filters    can change with time, necessitating      several measurements at the time of
  inventory.
) Reasonable estimation       of hidden inventories  of holdup to meet regulatory     requirements
  can be accomplished through good measurements and statistical         modeling.




*     KEY WOROSAN12           DOCUMENT      ANALYSIS                                                        15b   DEsCRIPTORS




6    AVAILABILITY          S7A7EMENT                                                                               17 SECURITY      CLASSIFICATION                            18 NUMBER        OF PAGES
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                                                                                                                           Unclassified
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